The torque exerted by the mouse's weight on the clock's minute hand is calculated to be 0.09163 N·m using the torque formula with force, radius, and the angle between them.
To determine the torque exerted by the mouse's weight on the clock's minute hand when it is 10 minutes past the hour, we need to apply the formula:
Torque (τ) = r × F × sin(θ)
Here:
r is the radius (distance from the axis to the point where the force is applied), which is 17 cm or 0.17 m. F is the force, which is the weight of the mouse. The weight is given by the mass times the acceleration due to gravity: F = m × g = 0.055 kg × 9.8 m/s² = 0.539 N. θ is the angle between the force and the lever arm. At 10 minutes past the hour, the minute hand is horizontal, and the force of gravity acts vertically, so θ = 90° (sin(90°) = 1).Substituting these values into the formula:
τ = 0.17 m × 0.539 N × 1 = 0.09163 N·m.
Thus, the torque exerted by the mouse's weight about the rotation axis of the clock hand is 0.09163 N·m.
What is the basic atomic difference between isotopes of the same element?
Temperature is a measure of how much the atoms in a substance are moving. Why is a substance hotter in the gas state than in the liquid state?
A substance is hotter in its gas state because the particles have more freedom to move, resulting in higher average kinetic energy and temperature. The transition from liquid to gas involves the absorption of heat, which is converted into kinetic energy of the gas particles.
Temperature is a measure of the average kinetic energy of the particles within a substance, which reflects how much the atoms in a substance are moving. Substances in the gas state are hotter than in the liquid state because the particles in a gas are moving freely at high speeds, colliding with each other and their surroundings. This high-speed, random motion contributes to a higher average kinetic energy and therefore a higher temperature. In contrast, particles in a liquid are closer together and while they can move past each other, they are not as free to move as in a gas.
The transition from liquid to gas requires energy, typically in the form of heat, which further increases the motion of the particles. When a liquid vaporizes to become a gas, it absorbs heat, which then gets converted into the kinetic energy of the gas particles, leading to higher temperatures. This also explains why many chemical reactions proceed faster at higher temperatures, as the increased motion of particles leads to more frequent and energetic collisions, which are necessary for reactions to occur.
How to calculate displacement in physics?
Answer:Displacement is the distance travelled in a specified direction.
:. Displacement = distance x time
Explanation:
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What are the SI base units for length and mass?
kilometer and gram
meter and gram
meter and kilogram
kilometer and kilogram
Answer:
meter and kilogram
Explanation:
As we know that there are seven fundamental SI units which are used to fine derived units
these are as following
1). Mass - Kilogram
2). Length - meter
3). Time - Seconds
4). Electric Current - Ampere
5). Amount of substance - Moles
6). Intensity of light - Candela
7). Temperature - Kelvin
German scientist alfred wegener is best known for what hypothesis
Answer:
Continental Drift Hypothesis.Explanation:
Alfred Lothar Wegener (1880-1930) was a German meteorologist and geophysicist who completed the first hypothesis about Continental Drift. He explained that the continents had onced formed a single mass, a single "continent" and then all began to break apart, until reach their presents positions.
So, according to Wegener's hypothesis, all the land on Earth was part of a single and unique mass, which was separated with the years.
Therefore, Alfred Wegener was best known for the Continental Drift Hypothesis.
A 48 kg girl is standing on a chair. What is the force exerted by the chair?
What is the major role of the Nuclear Regulatory Commission? Monitoring and regulating nuclear waste generated and issues associated to it in the US. Stopping nuclear research in other countries. Preventing a nuclear attack on the US. Investigating new uses for nuclear materials in the US.
what is the acceleration of a 5 kg mass pushed by a 10 n force?
The total amount of energy and mass in the universe is _____. always changing slowly increasing constant slowly decreasing
Answer:
constant
Explanation:
The universe is an isolated system. In thermodynamics, an isolated system is a system that does not exchange neither matter (mass) nor energy with the external surroundings.
As a consequence, the energy and mass of an isolated system is always constant (because it cannot be exchanged with the outside): this is known as law of conservation of energy, and it can be applied to the universe as well, since it is an isolated system.
So, the correct answer is
The total amount of energy and mass in the universe is constant
A rock held by a person above the floor, but not dropped, is an example of which of newton's laws?
A ramp leading to the freeway overpass is 210 feet long and rises 31 feet. what is the measure of the angle formed between the ramp and the freeway?
Final answer:
To find the measure of the angle formed between the ramp and the freeway, we can use trigonometry.
Explanation:
To find the measure of the angle formed between the ramp and the freeway, we can use trigonometry. The angle can be found using the inverse tangent function, which relates the length of the side opposite the angle (the rise) to the length of the side adjacent to the angle (the length of the ramp).
We can use the formula:
angle = arctan(rise/run)
In this case, the rise is 31 feet and the run is 210 feet. Plugging these values into the formula, we get:
angle = arctan(31/210)
Using a calculator, we find that the measure of the angle is approximately 8.2 degrees.
How do I find magnitude of acceleration?
Final answer:
To find the magnitude of acceleration, use kinematic equations or Newton's second law if the force and mass are known, or use the Pythagorean theorem for resultant acceleration in two dimensions.
Explanation:
To find the magnitude of acceleration, one needs to use kinematic equations that relate acceleration with other motion variables (such as velocity, time, and displacement) or use Newton's second law if the forces acting on the object are known.
For example, consider Newton's second law which states that the force applied on an object is equal to the mass of the object times its acceleration (F = ma). If you know the mass (m) and the net external force (F), you can solve for the acceleration (a) by rearranging the equation to a = F/m.
In the case where motion is in two dimensions, the acceleration components along the x- and y-axes can be represented as ax and ay. If we are dealing with gravitational acceleration, on Earth it is typically approximated as 9.8 m/s² directed downwards. To find the magnitude of a resultant acceleration vector, you can use the Pythagorean theorem if you have its components: a = √(ax² + ay²).
You are walking along a small country road one foggy morning and come to an intersection. while you are crossing, you hear an ambulance siren. as a paramedic, you know that the siren sounds at a frequency of 5.87 khz. but, as an amateur musician with perfect pitch, you can tell that the frequency you are hearing is actually 5.29 khz. is the ambulance moving toward or away from you?
a baseball rolls off a 0.70 m high desk and strikes the floor 0.25m away from the base of the desk. how fast was the ball rolling?
please help... I don't understand this :(
By breaking the problem into vertical and horizontal components, we determined the time the ball was in the air and used it to calculate the horizontal velocity. The ball was rolling off the desk at approximately 0.66 m/s. This involves understanding projectile motion in physics.
To determine how fast the baseball was rolling off the desk, we need to use principles of projectile motion. We can break the motion into horizontal (x-direction) and vertical (y-direction) components.
Vertical (y-direction) Analysis:
Initial vertical velocity (u_y) is 0 m/s because the ball is rolling horizontally off the desk.Height of the desk (h) = 0.70 m.Acceleration due to gravity (g) = 9.8 m/s².We can use the kinematic equation: h = (1/2) * g * t² to find the time (t) it takes for the ball to hit the ground.Solving for t: 0.70 = 0.5 * 9.8 * t² → t² = (0.70 * 2) / 9.8 → t² ≈ 0.143 → t ≈ 0.38 s.Horizontal (x-direction) Analysis:
The horizontal distance (d) the ball travels is 0.25 m.The time in the air is the same as calculated in the vertical direction, t ≈ 0.38 s.The horizontal velocity (v_x) can be found using the equation: d = v_x * t.Solving for v_x: 0.25 = v_x * 0.38 → v_x ≈ 0.25 / 0.38 → v_x ≈ 0.66 m/s.Therefore, the ball was rolling off the desk at approximately 0.66 m/s.
What is the quality of the sound of a fire truck’s siren when it moves toward a stationary hearer?
What is the quality of the sound of a fire truck’s siren when it moves away from a stationary hearer?
Its Low Pitched
Answer:
The pitch increases.
Explanation:
According to the Doppler effect, the apparent frequency of the waves is different when there is relative motion between the source and the observer. When the source and observer approach, the apparent frequency (pitch) increases whereas it decreases when they recede away.
Thus, when a fire truck moves towards a stationary hearer, the pitch of the siren appears to increase.
The speed of sound in air is 331 m/s. what is the plane's speed in terms of the speed of sound?
The plane's speed in relation to the speed of sound, called Mach number, can be determined by dividing the plane's speed by the speed of sound.
Explanation:The speed of a plane in relation to the speed of sound, often referred to as Mach number, is determined by dividing the plane's speed by the speed of sound. An airplane flying at the speed of sound would thus be flying at Mach 1. If the plane is flying faster than the speed of sound, it is considered to be supersonic. For instance, if the speed of the plane is 662 m/s, that would be Mach 2 as it is twice the speed of sound which is 331 m/s.
Therefore, to find the plane's speed in terms of the speed of sound, you would divide the plane's speed by 331 m/s.
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To express the plane's speed in terms of the speed of sound, we use the Mach number. If the speed of sound in air is 340 m/s, a plane traveling at Mach 2.00 is moving at 680 m/s (2 x 340 m/s).
The speed of sound in air is variable, depending on temperature and atmospheric pressure but is approximately 340 m/s at sea level at 21°C. When we talk about aircraft speeds, we often refer to their speed in terms of their Mach number, which is the ratio of the object's speed to the speed of sound. For instance, an aircraft flying at Mach 1 is traveling exactly at the speed of sound for those conditions, while Mach 2 indicates it is traveling twice the speed of sound. Therefore, if the speed of sound is 340 m/s and a plane is traveling at Mach 2, its speed is simply calculated by doubling the speed of sound, which gives us a velocity of 680 m/s. This is why an observer might hear a sonic boom without seeing the plane: it has passed by before the sound reaches the observer. Changes in air temperature also affect the speed of sound, so when a supersonic aircraft transitions from warmer to colder air, adjustments in velocity must be made to maintain the same Mach number due to the changed speed of sound.
Two scientists are discussing their beliefs about something they cannot observe
Displacement vs distance
Distance is the length of the path traveled, while displacement is the straight-line distance between the initial and final position, considering both magnitude and direction.
Explanation:Distance is the length of the path traveled by an object, while displacement is the straight-line distance from the initial to the final position, regardless of the path taken. Displacement includes both magnitude and direction, whereas distance only considers magnitude.
For example, if a person walks 5 meters to the east and then 3 meters to the west, their displacement would be 2 meters to the east, as it considers the overall change in position. However, the total distance traveled would be 8 meters, as it accounts for the entire path traveled.
It is important to note that displacement is a vector quantity, meaning it has both magnitude and direction, while distance is a scalar quantity with only magnitude.
What kind of change does shot peening cause in a sheet of metal?
It will change shape because the comprehensive stress layer causing it to bend slightly. Thus, thinner material like sheet metal will apparently change its shape. This is usually the reason why someone/people would peen sheet metal. In addition, Shot peening is cold working process done to metal parts for fatigue resistance. And the process is done by placing the part surface into compression.
If a substance is changing from a vapor to a liquid, like steam on a mirror, it is said to be _______.
volatile
condensing
crystallized
changing pigmentation
Answer:
condensing
Explanation:
Condensing is the word used to indicate the change of state of a substance from vapor to liquid, as in this case. During condensation, the substance releases thermal energy to the environment, therefore the kinetic energy of the molecules in the vapor decreases until they become closer to each other and they start to be affected by the intermolecular forces and so the substance becomes a liquid.
Answer: condensing
Explanation: I took the test
true or false: objects fall toward earth at a rate of 9.8 m/s because of centripetal force.
The statement is false; objects fall toward Earth at roughly 9.8 m/s² due to gravity, not centripetal force. Gravity is a force that causes objects to accelerate towards the Earth, while centripetal force relates to circular motion.
Explanation:The statement that objects fall toward Earth at a rate of 9.8 m/s because of centripetal force is false. Objects in freefall near the Earth's surface accelerate downwards at approximately 9.8 m/s² due to the force of gravity, not centripetal force. Centripetal force is related to the circular motion of an object and is the force that acts on an object moving in a circular path, directed towards the center around which the object is moving.
It is important to note that the acceleration of 9.8 m/s², commonly represented as g, is somewhat an approximation. This value can slightly vary depending on the distance from the center of the Earth and the density of the Earth's crust in different locations. Nonetheless, for most practical purposes, especially in educational environments, g is considered to be a constant value.
Newton's Universal Theory of Gravity explains that this acceleration due to gravity is expected because the force of gravity, and thus the acceleration of an object, is inversely proportional to the square of its distance from the center of the Earth. Objects at or near the Earth's surface, like falling apples, typically experience this acceleration of 9.8 m/s².
How long will it take a shell fired from a cliff at an initial velocity of 800 m/s at an angle 30 degrees below the horizontal to reach the ground 150m below?
The shell will take about 0.34 seconds to reach the ground.
Step 1T is given as 800 m/s. The factors that would impact time are gravity and angle.
The factor of gravity (g) is a constant given as = 9.81. Any object on earth will accelerate at the speed of 9.81 meters per second if they are in a free fall.
Hence, T = 800Sin(30°) / g = 800 * 0.5
This is equals 400/9.81 = 40.773 or 40.78 seconds.
Step 2Given that the vertical velocity of the shell is zero because it is accelerating at an angle towards the earth, it will rise at an average speed that can be computed as:
1/2 (800sin30°) = 1/2 * 400 = 200m/s for Tsec and arise of H which is 8,156m.
Step 3The shell having risen falls from rest at the height given above.
S therefore, = 150 +H, that is 150 + 8,156m. This is equals to 8,306m.
Step 4Next, we compute for the Kinematics equation of distance in relation to time (t) where the initial speed is 0.
S = 1/2(gt)²
thus 8,306 = 0.5 * 9.81*t² with elementary cross multiplication and the and the squaring of both sides, we have
t = [tex]\sqrt{1693}[/tex]
t= 41.14608 which is approximately 41.12 seconds.
Because the time taken for the shell to rise and then to fall to the ground is the sum of T and t. the time taken to fall or the time taken for the shell to travel towards to the ground is:
t - T = 41.12 - 40.78
= 0.34 seconds
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A fugitive tries to hop on a freight train traveling at a constant speed of 5.0 m/s. Just as an empty box car passes him, the fugitive starts from rest and accelerates at a = 3.8 m/s2 to his maximum speed of 8.0 m/s.
A. The time to catch up to the empty box car is about 2.8 s
B. The distance traveled to reach the box car is about 14 m
Further explanationAcceleration is rate of change of velocity.
[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]
[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]
a = acceleration ( m/s² )
v = final velocity ( m/s )
u = initial velocity ( m/s )
t = time taken ( s )
d = distance ( m )
Let us now tackle the problem !
Given:
Acceleration of car = a = 3.8 m/s²
Initial Velocity of car = u = 0 m/s
Velocity of train = vt = 5.0 m/s
Unknown:
A . Time Taken = t = ?
B. Distance = d = ?
Solution:
Question A:Firstly, we calculate for the distance traveled by the car until it reaches a maximum speed of 8 m / s.
[tex]v^2 = u^2 + 2ad_1[/tex]
[tex]8^2 = 0^2 + 2(3.8)d_1[/tex]
[tex]64 = 7.6d_1[/tex]
[tex]\boxed {d_1 = \frac{160}{19} ~ m}[/tex]
Next , we find time taken for the car to reach this maximum speed
[tex]v = u + a t[/tex]
[tex]8 = 0 + 3.8t'[/tex]
[tex]t' = 8 \div 3.8[/tex]
[tex]\boxed {t' = \frac{40}{19} ~ s}[/tex]
When trains and cars meet, then
[tex]d_{train} = d_{car}[/tex]
[tex]v_t \times t = d_1 + v_{max} \times (t - t')[/tex]
[tex]5t = \frac{160}{19} + 8(t - \frac{40}{19})[/tex]
[tex]5t = \frac{160}{19} + 8t - \frac{320}{19}[/tex]
[tex]5t = -\frac{160}{19} + 8t[/tex]
[tex]8t - 5t = \frac{160}{19}[/tex]
[tex]3t = \frac{160}{19}[/tex]
[tex]t = \frac{160}{19} \div 3[/tex]
[tex]t = \frac{160}{57} ~ s[/tex]
[tex]\large {\boxed {t \approx 2.8 ~ s} }[/tex]
Question B:[tex]d_{car} = -\frac{160}{19} + 8t[/tex]
[tex]d_{car} = -\frac{160}{19} + 8 \times \frac{160}{57} [/tex]
[tex]d_{car} = \frac{800}{57} ~ m[/tex]
[tex]\large {\boxed {d_{car} \approx 14 ~ m} }[/tex]
Learn moreVelocity of Runner : https://brainly.com/question/3813437Kinetic Energy : https://brainly.com/question/692781Acceleration : https://brainly.com/question/2283922The Speed of Car : https://brainly.com/question/568302Answer detailsGrade: High School
Subject: Physics
Chapter: Kinematics
Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate
A box of mass 5.0 kg is accelerated from rest by a force across a floor at a rate of 2.0 m/s2 for 7.0 s. find the net work done on the box.
Answer:
Work done on the box is 490 joules.
Explanation:
It is given that,
Mass of the box, m = 5 kg
Initial speed of the box, u = 0
Acceleration of the box, [tex]a=2\ m/s^2[/tex]
Time taken, t = 7 s
The force is calculate using the product of mass and acceleration. It is given by :
F = ma
[tex]F=5\ kg\times 2\ m/s^2=10\ N[/tex]
Let d is the distance covered by the box. Using the equation of motion as :
[tex]d=ut+\dfrac{1}{2}at^2[/tex]
[tex]d=\dfrac{1}{2}\times 2\ m/s^2\times (7\ s)^2[/tex]
d = 49 m
The product of force and distance is equal to the work done on the box. It is given by :
[tex]W=F\times d[/tex]
[tex]W=10\ N\times 49\ m[/tex]
W = 490 joules
So, the work done on the box is 490 Joules. Hence, this is the required solution.
The net work done on the box weighing 5.0 kg and accelerated from rest by a force across a floor is 490 Nm.
Given the following data:
Initial velocity = 0 m/s (since the box starts from rest).Mass of box = 5 kgAcceleration = 2 [tex]m/s^2[/tex]Time = 7 secondsTo find the net work done on the box:
First of all, we would determine the force acting on the box:
[tex]Force = Mass[/tex] × [tex]acceleration[/tex]
[tex]Force = 5[/tex] × [tex]2[/tex]
Force = 10 Newton
Next, we would use the second equation of motion to determine the distance traveled by the box:
[tex]S = ut+ \frac{1}{2}at^2[/tex]
Where:
S is the displacement or distance traveled.u is the initial velocity.a is the acceleration.t is the time measured in seconds.Substituting the given parameters into the formula, we have;
[tex]S = 0(7)+ \frac{1}{2}(2)(7^2)\\\\S = 0 + 49[/tex]
Distance, S = 49 meters.
Now, we can determine the net work done on the box:
[tex]Work\; done = Force[/tex] × [tex]distance[/tex]
[tex]Work\; done = 10[/tex] × [tex]49[/tex]
Work done = 490 Nm
Therefore, the net work done on the box is 490 Nm.
A car travels in straight line for 5.5 h at a constant speed of 59km/h. What is its acceleration?
A------turns about a fixed point called a fulcrum.
Answer:
lever
Explanation:
What information and measurements would you need to calculate the rate of movement?
Final answer:
To calculate the rate of movement, you need displacement and time to determine velocity and average velocity. Acceleration requires additional time and displacement data, used with kinematic equations. In analyzing motion, combining displacements and velocities in two dimensions is essential to determine overall movement parameters.
Explanation:
To calculate the rate of movement, you would need information on both displacement and time. These two measurements allow you to determine velocity, average velocity, and acceleration. Velocity is the rate of change of displacement with time, and it can be calculated if you know the displacement of an object and the time it took to cover that displacement. To find average velocity, you divide the total displacement by the total time.
In cases involving acceleration, you would need additional displacement and time data to calculate how quickly the velocity is changing. Kinematic equations are particularly useful for this purpose. One of the basic kinematic equations, v = u + at (where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time), can be used to find the final velocity of an object.
To determine negative acceleration, also known as deceleration, you would again use kinematic equations. The kinematic equation v^2 = u^2 + 2as (where s is the displacement) can be rearranged to solve for acceleration.
In Physics, especially in Advanced Placement (AP) courses, describing motion in two dimensions often requires combining displacements and velocities in various directions. This is done to calculate the overall displacement and average velocity. Measurements like the total time in the air, the maximum height reached, and the horizontal distance covered are critical when analyzing projectile motions or any two-dimensional movements.
Finally, to measure momentum, one would have to measure mass and velocity. The momentum of a body is given by the product of its mass and velocity. Depending on the experiment, you might measure the force over the duration of a collision using sensors or high-speed cameras to determine the initial and final velocities of the objects involved.
A bicyclist in the Tour de France crests a mountain pass as he moves at 18 km/h. At the bottom, 4.0 km farther, his speed is at 75 km/h. What is the average acceleration (in m/s^2) while riding down the mountain?
We are given:
v0 = initial velocity = 18 km/h
d = distance = 4 km
v = final velocity = 75 km/h
a =?
We can solve this problem by using the formula:
v^2 = v0^2 + 2 a d
75^2 = 18^2 + 2 (a) * 4
5625 = 324 + 8a
a = 662.625 km/h^2
How far will sound travel in 60 seconds if the temeperature is 20c?
Which of the following is a natural resource that is used to produce margarine?
butter
water
hydrogenated oil
plants
the answer is water and plants
Hydrogenated oil, derived from plants, is used to produce margarine. The hydrogenation process converts liquid vegetable oils into solid or semi-solid fats, making them more stable for use in products like margarine.
Explanation:The natural resource used to produce margarine is hydrogenated oil. Hydrogenation is a chemical process that converts liquid vegetable oils into solid or semi-solid fats, which are more stable. Margarine is made by reacting these oils (from plants like sunflowers, canola, or soy) with hydrogen. This is in the presence of a catalyst, usually a metal. The hydrogenation process solidifies the oils and changes their nutritional profile.
While water can be a component in the production process and plants are the source of the vegetable oils used, it's the hydrogenated oil that is the primary ingredient.
Butter, on the other hand, is not used in the production of margarine as it is an animal product and margarine is created as a plant-based alternative to it.
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