Answer:
0.09852 seconds
Explanation:
[tex]\mu[/tex] = Linear density = 0.0292 kg/m
[tex]T_A[/tex] = Tesnsion in string A = [tex]33\times 10^2\ N[/tex]
[tex]T_B[/tex] = Tesnsion in string B = [tex]3.76\times 10^2\ N[/tex]
t = Time taken till the pulses pass each other
Velocity of wave in a string is given by
[tex]v_A=\sqrt{\dfrac{T_A}{\mu}}\\\Rightarrow v_A=\sqrt{\dfrac{33\times 10^2}{0.0292}}[/tex]
[tex]v_B=\sqrt{\dfrac{T_2}{\mu}}\\\Rightarrow v_B=\sqrt{\dfrac{3.76\times 10^2}{0.0292}}[/tex]
[tex]Distance=Speed\times Time[/tex]
[tex]L=(v_A+v_B)t\\\Rightarrow t=\dfrac{L}{v_A+v_B}\\\Rightarrow t=\dfrac{44.3}{\sqrt{\dfrac{33\times 10^2}{0.0292}}+\sqrt{\dfrac{3.76\times 10^2}{0.0292}}}\\\Rightarrow t=0.09852\ s[/tex]
The time taken is 0.09852 seconds
Answer:
[tex]t=0.0985\ s[/tex]
Explanation:
Given:
length of each wire, [tex]l_a=l_b=44.3\ m[/tex]linear mass density of each wire, [tex]\mu_a=\mu_b=0.0292\ kg.m^{-1}[/tex]tension in wire A, [tex]T_a=3300\ N[/tex]tension in wire B, [tex]T_a=376\ N[/tex]Now, the velocity of the wave pulse in the stretched spring is given as:
FOR A:
[tex]v_a=\sqrt{\frac{T_a}{\mu_a} }[/tex]
[tex]v_a=\sqrt{\frac{3300}{0.0292} }[/tex]
[tex]v_a=336.175\ m.s^{-1}[/tex]
FOR B:
[tex]v_b=\sqrt{\frac{T_b}{\mu_b} }[/tex]
[tex]v_b=\sqrt{\frac{376}{0.0292} }[/tex]
[tex]v_b=113.476\ m.s^{-1}[/tex]
Let the distance at which the wave of A meets the wave of B be x from left then the distance from B is (44.3-x) meters.
Now the time taken is constant:
[tex]t=\frac{x}{v_a} =\frac{x-44.3}{v_b}[/tex]
[tex]\frac{x}{336.175} =\frac{x-44.3}{113.476}[/tex]
[tex]x=33.12\ m[/tex] is the distance travelled by pulse in wire A in when the pulse in the wire B meets
Now the time taken to travel this distance by pulse in wire A:
[tex]t=\frac{x}{v_a}[/tex]
[tex]t=\frac{33.12}{336.175}[/tex]
[tex]t=0.0985\ s[/tex] is the time taken by the two waves to pass each other.
A man cleaning his apartment pushes a vac-uum cleaner with a force of magnitude 42.8 N.The force makes an angle of 16.5◦with the hor-izontal floor. The vacuum cleaner is pushed2.62 m to the right along the floor.Calculate the work done by the 42.8 N force.Answer in units of J.
Answer:
107.52 J
Explanation:
force (f) = 42.8 N
angle of force (θ) = 16.5 °
distance (d) = 2.62 m
find the work done.
work done = force x distance
resolving the force we have = 42.8 x cos (16.5) = 41.04 N
work done = 41.04 x 2.62 = 107.52 J
A package of aluminum foil is 59.3 yd long, 13 in. wide, and 0.00040 in. thick. If aluminum has a density of 2.70 g/cm3, what is the mass, in grams, of the foil?
Answer:
493.02 g.
Explanation:
Density = mass/volume
mass = density×volume
m = D×V ............................ Equation 1
m = mass of the aluminum foil, D = Density of the aluminum foil, V = volume of the aluminum foil.
V = L×W×H................... Equation 2
Where L = length of the aluminum foil, W = wide of the aluminum foil, H = thickness of the aluminum foil.
Given: L = 59.3 yd = 59.3×0.9144 m = 54.224 m, W = 13 in = 13×0.0254 m = 0.3302 m, H = 0.00040 in = 0.00040×0.0254 m = 0.0000102 m.
Substituting into equation 2
V = 54.224×0.3302×0.0000102
V = 0.0001826 m³ = (0.0001826×1000000) cm³
V = 182.6 cm³
Also given D = 2.70 g/cm³
Substitute into equation 1
m = 2.7×182.6
m = 493.02 g.
The mass in grams of the foil = 493.02 g.
A 3.8 kg block is projected at 4.4 m/s up a plane that is inclined at 37o with the horizontal. How far up along the plane does the block go:___________
(a) if the plane is frictionless and
(b) if the coefficient of kinetic friction between the block and the plane is 0.47
(c) what is thermal energy generated by friction?
Answer:
Explanation:
a) Deceleration due to gravity along the inclined plane is given by:
g*Sin(∅)= 9.8*Sin(37)=5.9 m/s^2.
Since acceleration is constant, we can use equation of motion along the plane. [tex]V^{2} = U^{2} +2as[/tex]
where V: final velocity, U:initial Velocity, a:Acceleration and s:distance
0=[tex]4.4^{2} + 2*-5.9*s[/tex] (-ve because it is against gravity)
It will go 1.64 meters up the plane
b) Force due to friction = Coeff. of friction * Normal Force
Normal Force = mg*Cos(∅) = 9.8*3.8*Cos(37) = 29.75;
Coeff of friction = 0.47;
Force due to friction = 0.47*29.75 = 13.98 N
Force due to gravity : 3.8*5.9 = 22.42;
Total force after adding friction = 22.42 + 13.98 = 36.4 N
New Acceleration = 36.4/3.8 = 9.58;
Applying the equation of motion used above with acceleration = 9.58;
It will go 1.01 meters up the plane.
c) Thermal energy due to friction = Max potential energy without friction - max potential energy after friction.
Potential energy w.o friction(m*g*h) = 3.9 * 9.8 * 1.64*Sin(37) = 37.72 Joules
Potential energy with friction(m*g*h)= 3.9 * 9.8 * 1.01*Sin(37) = 23.23 Joules
Energy due to friction = 37.72 - 23.23 = 14.49 Joules
If you place a free electron and a free proton in the same electric field, how will the forces acting on them compare? 82. How will the accelerations of the proton and the electron in the preceding problem compare? 83. How will the directions of travel compare for the electron and the proton in the preceding problem?
Answer:
the force experienced by both particles will be of same magnitude as the magnitude of charge is same for both particles but with different sign, the acceleration of both particles will be same in magnitude but opposite in direction, the direction of free electron will be opposite to the direction of electric field whereas the direction of proton will be in the direction of electric field,
Explanation:
the force experienced by both particles can be calculated by the formula
F=|q|E
the acceleration can be calculated by Newton's 2nd law i.e F=ma
the direction of electric field is always towards the positive charge so proton will be directed towards electric field and free electron will be directed away from the electric field.
An object on a vertical spring oscillates up and down in simple harmonic motion with an angular frequency of 14.2 rad/s. Calculate the distance d by which the spring stretches from its unstrained length when the object is allowed to hang stationary from it.
Answer:
0.04865 m
Explanation:
k = Spring Constant
m = Mass
d = Distance
g = Acceleration due to gravity = 9.81 m/s²
Angular frequency is given by
[tex]\omega=\sqrt{\dfrac{k}{m}}\\\Rightarrow \dfrac{k}{m}=\omega^2\\\Rightarrow \dfrac{k}{m}=14.2^2[/tex]
At equilibrium we have
[tex]kd=mg\\\Rightarrow d=\dfrac{mg}{k}\\\Rightarrow d=\dfrac{g}{\omega^2}\\\Rightarrow d=\dfrac{9.81}{14.2^2}\\\Rightarrow d=0.04865\ m[/tex]
The distance by which the spring stretches from its unstrained length is 0.04865 m
Bicyclists in the Tour de France reach speeds of 34.0 miles per hour (mi/h) on flat sections of the road. What is this speed in (a) kilometers per hour (km/h) and (b) meters per second (m/s)
Answer: a) The speed in km/hr is 54.7.
b) The speed in m/s is 15.2
Explanation:
a) The conversion used from miles to km is:
1 mile = 1.61 km
34.0 miles= [tex]\frac{1.61}{1}\times 34.0=54.7km[/tex]
We are asked: 34.0 miles/hr = ? km/hr
Thus 34.0 miles/hr = [tex]\frac{54.7}{1}=54.7km/hr[/tex]
Therefore, the speed in kilometer per hour is 54.7 km/hr
b) The conversion used from miles to m is:
1 mile = 1610 m
34.0 miles= [tex]\frac{1610}{1}\times 34.0=54740m[/tex]
The conversion used from hour to sec is:
1 hour = 3600 sec
We are asked: 34.0 miles/hr = ? m/s
Thus 34.0 miles/hr = [tex]\frac{54740m}{3600s}=15.2m/s[/tex]
Therefore, the speed in meters per second is 15.2 m/s
Final answer:
Bicyclists in the Tour de France traveling at 34.0 mi/h have a speed of approximately 54.72 km/h and 15.20 m/s after conversion.
Explanation:
To convert the speed of bicyclists in the Tour de France from miles per hour to kilometers per hour and meters per second, we can use the following conversion factors:
1 mile = 1.60934 kilometers
1 hour = 3600 seconds
(a) To convert 34.0 mi/h to km/h, multiply by the conversion factor:
34.0 mi/h imes 1.60934 km/mi = 54.7176 km/h
(b) To convert 54.7176 km/h to m/s, multiply by the conversion factor:
54.7176 km/h imes (1000 m / 1 km) imes (1 h / 3600 s) = 15.199 m/s
Therefore, a speed of 34.0 mi/h is approximately 54.72 km/h and 15.20 m/s.
How much work, in kJ, can a spring whose spring constant is 6 kN/cm produce after it has been compressed 3 cm from its unloaded length?
Final answer:
The spring can produce 0.270 kJ of work after it has been compressed 3 cm from its unloaded length, with a spring constant of 6 kN/cm.
Explanation:
The work done by a spring is given by the expression ½ kx², where k is the spring constant and x is the displacement from the spring's equilibrium position. In this case, we are given a spring constant of 6 kN/cm and a compression of 3 cm. First, convert the spring constant to N/m by multiplying by 10³ (since 1 kN = 10³ N and 1 cm = 10⁻² m), which gives us 600,000 N/m. The work can then be calculated as:
W = ½ kx² = ½ (600,000 N/m) (0.03 m)² = 270 J
Convert joules to kilojoules, 1 kJ = 1,000 J, gives:
W = 0.270 kJ
Therefore, the spring can produce 0.270 kJ of work after being compressed 3 cm from its unloaded length.
In one cycle, a heat engine takes in 1000 J of heat from a high-temperature reservoir, releases 600 J of heat to a lower-temperature reservoir, and does 400 J of work. What is its efficiency?
Answer:
η = 40 %
Explanation:
Given that
Qa ,Heat addition= 1000 J
Qr,Heat rejection= 600 J
Work done ,W= 400 J
We know that ,efficiency of a engine given as
[tex]\eta=\dfrac{W(net)}{Q(heat\ addition)}[/tex]
Now by putting the values in the above equation ,then we get
[tex]\eta=\dfrac{400}{1000}[/tex]
η = 0.4
The efficiency in percentage is given as
η = 0.4 x 100 %
η = 40 %
Therefore the answer will be 40%.
The efficiency of the heat engine is calculated using the formula Efficiency = W/Q(in), which gives an efficiency of 40% given the provided values.
To determine the efficiency (e) of a heat engine, we use the formula:
Efficiency =W/Q(in)where W is the work done by the engine and Q(in)is the heat absorbed from the high-temperature reservoir.
Heat absorbed (Q(in)): 1000 JHeat released (Q(out)): 600 JWork done (W): 400 JUsing the values:
Efficiency = 400 J/1000J= 0.4 or 40%Thus, the efficiency of the heat engine is 40%.
What type of UTP cabling is used in building open-air returns to reduce the amount of toxic components emitted into the air if a fire should occur?
Answer:
Plenum cabling
Explanation
As the plenum cabling are fire resistent so it will not cause the toxic components in case of fire.
A sidereal day is the time it takes for
A. the Sun to come back to the same position in the sky.
B. the stars to come back to the same positions in the sky.
C. the Moon to come back to the same positions in the sky
Answer:
B. the stars to come back to the same positions in the sky.
Explanation:
In fact, the solar day is equivalent to more than a rotation, because when the point has turned completely, it is not, as it should, in the same position with respect to the Sun.
The reason for this is that while performing the rotation, the Earth simultaneously moved following its orbit around the Sun.
When the reference point completed its rotation, the Earth already moved almost 2,500,000 km., So that to see the Sun again it will be necessary to turn a little more.
Solar day is more than a rotation. The sidereal or sidereal day, commonly used by astronomers, is also based on the rotation of the Earth; but in this case a distant star is taken as a reference (sidereal comes from the Latin sidus which means "star").
A child who does not seek proximity to the mother and, after she leaves the room, does not look distressed is exhibiting a(n) __________.
Answer:
Avoidant attachment pattern
Explanation:
The Attachment theory proposes that there are 4 attachment styles:
Secure attachment
Anxious attachment
Avoidant attachment
Anxious-Avoidant attachment
A child who does not seek their mother when they leave and are unbothered by the fact that the mother is not around shows the avoidant attachment pattern. The child is independent and self-directed, thus does not seek intimacy. These types of people are assumed to be fearful or avoidant when it comes to intimacy and commitment, as the theory suggests.
Differentiating it from the other style:
Secure attachment pattern show comfort in intimacy. They easily display interest to other parties, but at the same time, they do not necessarily seek intimacy as they are capable of being alone as well.
Anxious attachment on the other hand, is more like a needy and clingy type of behavior. They seek companionship more desperately and always needs reassurance.
Anxious-avoidant attachment is a more aggressive (in a defensive sense) type. They totally avoid commitment or any form of intimacy. What makes them different is the distrust. They do not trust anyone that tries to get close to them and can sometimes emotionally vent out, (verbally or physically) if anyone attempts to get to know them.
A 104-hp (shaft output) electric car is powered by an electric motor mounted in the engine compartment. If the motor has an average efficiency of 91 percent, determine the rate of heat supply by the motor to the engine compartment at full load.
Answer:
10.28571 hp
Explanation:
[tex]W_{shaft}[/tex] = Shaft output power = 104 hp
[tex]\eta[/tex] = Average efficiency = 91%
Electric work done rate is given by
[tex]W_{el}=\dfrac{W_{shaft}}{\eta}[/tex]
The rate of heat supply is given by
[tex]Q=W_{el}-W_{shaft}\\\Rightarrow Q=W_{shaft}(\dfrac{1}{\eta}-1)\\\Rightarrow Q=104(\dfrac{1}{0.91}-1)\\\Rightarrow Q=10.28571\ hp[/tex]
The heat supply by the motor to the engine compartment at full load is 10.28571 hp
A 120 kg hoop rolls along a horizontal floor so that the hoop's center of mass has a speed of 0.220 m/s. How much work must be done on the hoop to stop it?
Answer:W = -5.808J
Explanation:
Given:
Mass of hoop,m=120kg
Centre of mass speed of hoop,v= 0.220m/s
Rotational inertia,I= mr^2
I=120r^2
Kinetic energy of hoop= Linear kinetic energy + Rotational kinetic energy
K= (1/2mv^2) + (1/2Iw^2)
But w= (v/r)^2
K= (1/2mv^2) + (1/2×120r^2(v/r)^2)
K = (1/2×120×0.220^2) + (1/2×120×0.220^2)
K= 5.808J
To stop the hoop,its final kinetic energy must be zero,
Workdone = Kfinal-Kinitial = 0 - 5.808
W= -5.808J
Three objects are brought close to each other, two at a time.When objects A and B are brought together, they repel. When objectsB and C are brought together, they also repel. Which of thefollowing are true? (Select all that apply.) a. additional experiments must be performed todetermine the signs of hte cahrges.b. objects A and C possess charges of the samesign.c. one object is neutral.d. objects A and C possess charges of theoppostite sign.e. all three objects possess charges of thesame sign.
Answer:
e. all three objects possess charges of the same sign.
Explanation:
We know that objects with same polarity will repel each other while objects with opposite polarity will attract each other. Here objects A and B repel each other which means they possess the charge of same polarity. Objects B and C also repel each other which means that they also possess the same polarity (sign).
This means that A and C will also repel each other. All the three objects possess the charge with same polarity.
1 2 3 4 5 6 7 8 9 10 TIME REMAINING 59:49 Which changes would result in a decrease in the gravitational force between two objects? Check all that apply.
Answer:
increasing the distance between the objects
decreasing the mass of one of the objects
decreasing the mass of both objects
Explanation:
The complete question would be:
Which changes would result in a decrease in the gravitational force between two objects? Check all that apply.
increasing the distance between the objects
decreasing the distance between the objects
increasing the mass of one of the objects
increasing the mass of both objects
decreasing the mass of one of the objects
decreasing the mass of both objects
---------------------------------------------------------------------------------------
Gravitational force between two objects can be computed using the formula:
[tex]Fg = G\dfrac{Mm}{r^2}[/tex]
Where:
Fg is the gravitational force (Newtons or N)
G is the gravitational constant (6.674⋅10⁻¹¹N(m/kg)²)
M is the mass of one object (Kilograms or Kg)
m is the mass of the other object (Kilograms or Kg)
r is the distance between the two objects (m)
Now notice the relationship between the mass and gravitational force. Their relationship is direct, meaning as the value of one goes up, the other goes up and the reverse holds true. If the mass of one or both of the objects decreases, the gravitational force also decreases.
Now look at the relationship between the distance between the objects and the gravitational force-- they are indirect. This means that as one increases, the other decreases. So if we increase the distance between the objects, the gravitational force between them decreases as well.
Answer:
increasing the distance between the objects
decreasing the mass of one of the objects
decreasing the mass of both objects
Explanation:
Which of the following cloud services uses software to emulate hardware capabilities, such as to increase or decrease bandwidth or storage to meet changing needs?
Answer:
Iaas
Explanation:
Infrastructure as a service (IaaS) is an online service that supplies high-level APIs that are used to derefer various low-level information such as physical computing resources, location, data partitioning, scaling, protection, backup etc. of the underlying network infrastructure
Cloud computing is a cloud service that uses software to emulate hardware capabilities, such as increasing or decreasing bandwidth or storage to meet changing needs.
The cloud service that uses software to emulate hardware capabilities, such as increasing or decreasing bandwidth or storage to meet changing needs, is cloud computing.
In cloud computing, virtualization technology is used to create virtual instances of the hardware resources, allowing them to be dynamically allocated or scaled up/down as needed.
For example, Amazon Web Services (AWS) offers a cloud service called (Elastic Compute Cloud) that allows users to create virtual servers with customizable specifications, such as CPU, memory, and storage.
Users can easily increase or decrease these resources based on their requirements, without the need for physical hardware changes.
Other cloud services like Microsoft Azure, G o o g l e Cloud Platform, and IBM Cloud also provide similar capabilities, allowing organizations to optimize their resource allocation and cost efficiency.
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The 1 kg box is sliding along a frictionless surface. It collides with and sticks to the 2 kg box. Afterward, the speed of the two boxes is _____
Answer:
The speed of the boxes are 1 m/s.
Explanation:
Given that,
Mass of box = 1 kg
Mass of another box = 2 kg
Suppose 1 kg box moves with 3 m/s speed.
We need to calculate the speed of the boxes
Using formula of conservation of momentum
[tex]m_{1}u_{1}+m_{2}u_{2}=(m_{1}+m_{2})v[/tex]
Where, u = initial velocity
v = final velocity
Put the value into the formula
[tex]1\times3+2\times0=(1+2)v[/tex]
[tex]v=\dfrac{3}{3}[/tex]
[tex]v=1\ m/s[/tex]
Hence, The speed of the boxes are 1 m/s.
After the collision, the speed of the two boxes will reduce due to lost in kinetic energy associated with inelastic collision.
The given parameters;
mass of the box, m = 1 kgmass of the second box, = 2 kgApply the principle of conservation of linear momentum to determine the final velocity of the two boxes after collision.
m₁u₁ + m₂u₂ = v(m₁ + m₂)
1(u₁) + 2u₂ = v(3)
u₁ + 2u₂ = 3v
Where;
u₁ and u₂ are the initial velocity of the first and second box respectively
v is the final velocity of the two boxes
Thus, we can conclude that after the collision, the speed of the two boxes will reduce due to lost in kinetic energy associated with inelastic collision.
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When an object is moved from rest at point A to rest at point B in a gravitational field, the net work done by the field depends on the mass of the object and
1. the nature of the external force moving the object from A to B.
2. the velocity of the object as it moves between A and B.
3. both the positions of A and B and the path taken between them.
4. the path taken between A and B only.
5. the positions of A and B only.
In a gravitational field, the net work done by the field when an object moves from rest at point A to rest at point B depends only on the positions of A and B, not the path taken or the object's velocity while moving.
Explanation:When an object moves from rest at point A to rest at point B in a gravitational field, the net work done by the field is dependent on the positions of A and B only (option 5). This is based on the principle of conservation of energy in physics. If we consider the gravitational field to be conservative, the work done is independent of the path taken, and depends only on the initial (A) and final points (B).
The mass of the object and the gravitational field strength will determine the gravitational potential energy at these points, hence affecting the work done when the object is moved. It does not depend on the nature of the external force moving the object or the velocity of the object while moving. These factors could affect the time it takes to move the object, but not the net work done by the gravitational field.
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The net work done by the field when an object is moved from rest at point A to rest at point B in a gravitational field depends on the nature of the external force moving the object from A to B, and both the positions of A and B and the path taken between them.
Explanation:The net work done by the field when an object is moved from rest at point A to rest at point B in a gravitational field depends on the nature of the external force moving the object from A to B, and both the positions of A and B and the path taken between them.
If the object is moved vertically upwards or downwards, the work done by the gravitational field will be positive or negative respectively. However, if the object is moved in a horizontal direction, there will be no work done by the field as there is no change in height.
Therefore, option 3, both the positions of A and B and the path taken between them, is the correct answer.
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They are adding steel components to the roof supports of the structure. We know that steel elongates when heated. At what temperature will steel elongate nine inches per 100 feet of length?
a) 500 degrees.
b) 1000 degrees.
c) 1500 degrees.
d) 2000 degrees.
Answer:
The change in temperature of 576.9°C will produce an elongation of 9 inches per feet in steel.
Explanation:
The formula for linear expansion of a material is:
ΔL = αLΔT
where, ΔL = change in length
L = Original length
ΔT = Change in temperature
α = coefficient of linear expansion
For steel, α = 13 x 10^-6 /°C
L = 100 ft
ΔL = (9 in)(1 ft/12 in) = 0.75 ft
Therefore,
0.75 ft = (13 x 10^-6 /°C)(100 ft)ΔT
ΔT = 576.9°C
Two points are located on a rigid wheel that is rotating with an increasing angular velocity about a fixed axis. The axis is perpendicular to the wheel at its center. Point 1 is located on the rim, and point 2 is halfway between the rim and the axis. At any given instant, which point (if either) has the greater_______.a) angular velocity.b) angular acceleration.c) tangential speed.d) tangential acceleration.e) centripetal acceleration.
Answer:
A. The angular velocity of Point 1 and Point 2 are the same
B. The angular acceleration is equal.
C. Tangential velocity of Point 1 is greater than Point 2
D. The tangential acceleration of point1 is greater than point 2
E. The centripetal acceleration of Point 2 is greater than point 1
Explanation:
- Since angular velocity is angular displacement of Point divided by time and since they are in the same line perpendicular to the axis, that means angular velocity is equal.
The tangential speed is the measure of how quickly an object is traveling along a circular path and two object with the same angular velocity but different radius would have different tangential speed.
-The tangential acceleration is the measure of how quickly the tangential velocity changes and is angular acceleration multiplied by the radius from the centre of circle so since point 1 has a bigger radius, it would have a greater tangential acceleration.
The centripetal acceleration is the effect on the body traveling in a circular path and is directed towards the center of the circle and it is inversely proportional to the radius so the bigger the radius the smaller the centripetal acceleration.
Point 1 on the rim of the wheel has the greater tangential speed, while both points have the same angular velocity and angular acceleration.
Explanation:In this scenario, point 1, located on the rim of the wheel, has the greater tangential speed (c) since it travels a larger circle with a larger radius in the same amount of time as point 2. However, both points have the same angular velocity (a) since they are both attached to the same rigid wheel and rotate at the same rate. Additionally, both points experience the same angular acceleration (b) since they are undergoing circular motion with the same angular speed. The tangential acceleration (d) and centripetal acceleration (e) are not required to answer the question as the problem does not provide information regarding the tangential or centripetal forces acting on the points.
The belt of one ramp moves at a constant speed such that a person who stands still on it leaves the ramp 64 s after getting on. Clifford is in a real hurry, however, and skips the speed ramp. Starting from rest with an acceleration of 0.37 m/s2, he cov- ers the same distance as the ramp does, but in one-fourth the time. What is the speed at which the belt of the ramp is moving?
Answer:
0.74 m/s
Explanation:
given,
time taken by the ramp to cover cliff , t = 64 s
acceleration = 0.37 m/s²
distance traveled by the belt
[tex]x = v_{belt}t_{belt}[/tex]
Clifford is moving with constant acceleration
[tex]x = v_ot + \dfrac{1}{2}at^2[/tex]...(1)
initial velocity is equal to zero
[tex]x =\dfrac{1}{2}at^2[/tex]........(2)
equating equation (1) and (2)
[tex]v_{belt}t_{belt}=\dfrac{1}{2}at^2[/tex]
[tex]v_{belt}t_{belt}=\dfrac{1}{2}a(\dfrac{1}{4}\times t_{belt})^2[/tex]
[tex]v_{belt}=\dfrac{1}{32}a t_{belt}[/tex]
[tex]v_{belt}=\dfrac{1}{32}\times 0.37 \times 64[/tex]
[tex]v_{belt}= 0.74\ m/s[/tex]
Speed of the belt is equal to 0.74 m/s
A person stands in a stationary canoe and throws a 5.16 kg stone with a velocity of 8.05 m/s at an angle of 31.0° above thehorizontal. The person and canoe have a combined mass of 105 kg.Ignoring air resistance and effects of the water, find thehorizontal recoil velocity (magnitude and direction) of the canoe.
magnitude m/s
direction ---Select--- opposite the horizontal component of the velocityof the stoneat right angles to the horizontal component ofthe velocity of the stonealong the horizontal component of the velocity ofthe stone
The recoil velocity of the canoe is calculated using conservation of momentum. The horizontal component of the stone's velocity is first determined, and the stone's momentum is then used to find the canoe's recoil. The direction of recoil is opposite to the stone's horizontal velocity component.
Explanation:The recoil velocity of a stationary object after projecting an object can be calculated using the principle of conservation of momentum.
Since the person and the canoe are initially motionless, the total momentum before the stone is thrown must be equal to the total momentum afterwards.
Step-by-Step Explanation
Calculate the horizontal component of the stone's velocity using the given angle and the initial velocity (vcos(31.0°)).Find the stone's momentum in the horizontal direction by multiplying its mass by the horizontal component of its velocity.Apply conservation of momentum: The momentum imparted to the stone will be equal in magnitude and opposite in direction to the momentum of the person and canoe.Calculate the recoil velocity of the canoe by dividing the stone's horizontal momentum by the mass of the person and canoe combined.The direction of the canoe's recoil will be opposite to the stone's horizontal component of velocity since momentum is conserved and no external horizontal forces are acting on the system.
The men's world record for swimming 1500.0 m in a long course pool (as of 2007) is 14 min 34.56 s. At this rate, how many seconds would it take to swim 0.700 miles (1 mi = 1609 m)? (1 mi = 1609 m.)
Answer:
It will take 667.239 sec to cover 0.7 miles
Explanation:
We have given the men's world record in swimming is 1500 m in 1 min 34.56 sec
So distance d = 1500 m
Time t = 14 min 34.56 sec
As 1 minute = 60 sec
So time t = [tex]14\times 60+34.56=888.56sec[/tex]
So speed [tex]v=\frac{distance}{time}=\frac{1500}{888.56}=1.688m/sec[/tex]
Now new distance d = 0.7 miles
As 1 miles = 1609 m
So 0.7 miles =[tex]0.7\times 1609=1126.3m[/tex]
So time taken [tex]t=\frac{distance}{velocity}=\frac{1126.3}{1.688}=667.239sec[/tex]
Point charge q1 and q2 both of 22nC are separated by a distance of 58cm along horizontal axis point a is located 40cm from q1 and 18 cm from q2. What is the magnitude and direction of the electric field at point a
Answer:
E = 4.01×10^6 N/C
direction is toward q2
Explanation:
q1 = q2 = 12micro-C = 12×10^-6C
r1 = 18cm = 0.18m
r2 = 40cm = 0.40m
k = 9×10^9
E1 = kq1/(r1)²
E1 = 3.33×10^6 N/C
E2 = kq2/(r2)²
E2 = 6.75×10^5 N/C
Enet = E1 + E2
= 3.33×10^6 + 6.75×10^5
= 4.01×10^6 N/C
direction is toward q2
Explain how neurons convey information using both electrical and chemical signals.
Answer:
Explanation:
Neurons communicate via both electrical signals and chemical signals. The electrical signals are action potentials, which transmit the information from one of a neuron to the other; the chemical signals are neurotransmitters, which transmit the information from one neuron to the next.
The electrical signal travels down the axon to the axon terminals where it tells the vesicles to release the neurotransmitters into the synaptic cleft which travel to the receptors of the receiving cell which releases the second messengers
Neurons convey information using both electrical and chemical signals. Electrical signaling occurs through the generation of action potentials, while chemical signaling occurs at the synapse through the release of neurotransmitter molecules.
Explanation:Neurons, specialized cells in the nervous system, convey information using both electrical and chemical signals. Electrical signaling occurs through the generation of action potentials, which are electrical impulses that travel along the neuron's axon. When a neuron is stimulated, a wave of depolarization is generated, leading to the opening of ion channels and a change in the neuron's membrane potential. This electrical event allows the action potential to propagate down the axon.
Chemical signaling, on the other hand, occurs at the synapse, the junction between two neurons. When an action potential reaches the axon terminal of the presynaptic neuron, it triggers the release of neurotransmitter molecules into the synapse. These neurotransmitters diffuse across the synaptic gap and bind to receptors on the postsynaptic neuron, generating a chemical signal. This signal can either excite or inhibit the postsynaptic neuron, depending on the type of neurotransmitter and receptor involved.
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In a certain city, electricity costs $ 0.13 per kW ⋅ h . What is the annual cost for electricity to power a lamppost for 8.00 h per day with a 100. W incandescent light bulb versus an energy efficient 25 W fluorescent bulb that produces the same amount of light? Assume 1 year = 365 days .
Answer:
37.96usd , 9.49usd
Explanation:
From the data given we have
cost of electricity= $0.13,
and annual cost of electricity is express as
Annual cost= power *hours*days*cost of electricity
note the unit of power must be in kilowatt(Kw),
a. to determine the cost of running 100w we first convert to kw
[tex]1w=0.001kw\\100w=0.1kw\\[/tex]
Hence the annual cost of running it 8.00 hours per day is calculated as
[tex]annual cost=0.1*8*365*0.13\\annual cost=37.96 USD[/tex]
b. to determine the cost of running 25w we first convert to kw
[tex]1w=0.001kw\\25w=0.025kw\\[/tex]
Hence the annual cost of running it 8.00 hours per day is calculated as [tex]annual cost=0.025*8*365*0.13\\annual cost=9.49 USD[/tex]
Hence from the answers we can conclude that less amount of money required to run the 25w incandescent bulb compare to the 100w
A cylindrical fuel rod of 2 cm in diameter is encased in a concentric tube and cooled by water. The fuel generates heat uniformly at a rate of 150 MW/m3. The convection heat transfer coefficient on the fuel rod is 5000 W/m2 .K, and the average temperature of the cooling water, sufficiently far from the fuel rod, is 70 o C. Determine the surface temperature of the fuel rod and discuss whether the value of the given convection heart transfer coefficient on the fuel rod is reasonable?
[tex]\rm 220^oC[/tex] is the surface temperature of the rod. The fuel must be kept below [tex]\rm 300^oC[/tex] to avoid reaching the cooling water from the critical heat flux and the temperature below that it is reasonable.
The average kinetic energy of particles in a medium, such as a gas, liquid, or solid, is measured as temperature. It is a basic physical characteristic that enables us to comprehend how hot or cold something is. Depending on the location, temperature is often measured using different scales, such as Celsius or Fahrenheit, or in scientific situations, Kelvin (K). Temperature, said simply, tells us how quickly the particles in a substance are moving. The substance is hotter or cooler depending on how quickly the particles are moving.
Heat generated = Heat transferred by convection + Heat conducted
[tex]\rm q_{gen }= q'' \times V\\\rm q_{gen} = 150 \times 10^{6 }W/m^3 \times \pi \times r^2\\\rm q_{conv} = h \times A \times (T_{s }- T )\\\rm q_{conv} = 5000 W/m^2\timesK \times2 \times \pi \times r \times L \times (T_s - T)\\\rm q_{cond} = k \times A \times (T_{s} - T) / L\rm 150 \times 10^6 \times \times \times r^2= 5000 \times 2 \times \pi \times r \timesL \times (T_{s} - T) + k \times 2 \times \times \times r \timesL \times (T_{s} - T) / L\\\rm T_{s }=220^oC[/tex]
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A(n) 10.7 g bullet is shot into a(n) 4588 g wooden block standing on a frictionless surface. The block, with the bullet in it, acquires a speed of 1.74 m/s. Calculate the speed of the bullet before striking the block. Answer in units of m/s
Final answer:
To find the speed of the bullet before striking the block, we can use the law of conservation of momentum. By setting the initial momentum equal to the final momentum, we can solve for the initial velocity of the bullet.
Explanation:
To solve this problem, we can use the law of conservation of momentum. Momentum is defined as the product of an object's mass and velocity. In this case, we know the mass and velocity of the wooden block and bullet after the collision, and we want to find the velocity of the bullet before the collision.
Using the law of conservation of momentum, we have:
Initial momentum = Final momentum
Mass of bullet * Initial velocity of bullet + Mass of block * Initial velocity of block = Mass of bullet * Final velocity of bullet + Mass of block * Final velocity of block
Substituting the given values, we have:
(0.0107 kg)(Initial velocity of bullet) + (4.588 kg)(0 m/s) = (0.0107 kg)(1.74 m/s) + (4.588 kg)(1.74 m/s)
Simplifying the equation and solving for the initial velocity of the bullet, we get:
Initial velocity of bullet = 1.74 m/s - (4.588 kg)(1.74 m/s) / 0.0107 kg
Calculating the value, we find that the initial velocity of the bullet was 271.36 m/s.
After inspecting all of 55,000 kg of meat stored at the Wurst Sausage Company, it was found that 45,000 kg of the meat was spoiled. This data is described as a:A. Statistic B. Parameter
Answer:
B. Parameter.
Explanation:
After inspecting all of 55,000 kg of meat stored at the Wurst Sausage Company, it was found that 45,000 kg of the meat was spoiled.
The data above is described as a parameter because the data describes the entire population (the meat). the difference between statistic and parameters are statistic is used to describe a sample whereas parameter is used to describe the population.
The data indicating that 45,000 kg out of 55,000 kg of meat was spoiled at the Wurst Sausage Company is considered a parameter. This is because it describes the entirety of the meat stored.
Explanation:In this situation, the information about the 55,000 kg of meat, of which 45,000 kg was spoiled, is described as a parameter. A parameter is a number that describes a population, in this case, the entirety of meat stored at the Wurst Sausage Company. Whereas a statistic is a numeral that describes a sample, in this case, if they only inspected a portion of the meat storage, then the result would be a statistic.
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A negative charge moves in the direction of an electric field. Which of the following statements are true? Che?
The potential energy associated with the charge increases.
The electric field does not do any work on the charge.
The potential energy associated with the charge decreases.
The electric field does negative work on the charge.
The electric field does positive work on the charge.
A negative charge moving in the direction of an electric field will have its potential energy increased and the electric field will do negative work on the charge.
When a negative charge moves in the direction of an electric field, it experiences a force in the opposite direction to the electric field. This force does work on the charge, but since the charge is negative and the electric field does work in the direction opposite to the charge's movement, several things happen:
The potential energy associated with the charge increases because it is moving to a region of higher electric potential due to its negative charge.The electric field does negative work on the charge, which is why the potential energy of the charge increases.Since the potential energy increases, and assuming no kinetic energy is added, the electric field does not do any positive work on the charge; the work done by the electric field is negative.Therefore, out of the provided statements, the ones that are true are:
The potential energy associated with the charge increases.The electric field does negative work on the charge.