A hollow metal ball hangs on a long massless string. The device is driven by a small side-to-side oscillator with a constant very small amplitude and an adjustable frequency. The driver begins to oscillate at a very low frequency. The driver's frequency is then made to increase slowly and steadily. The frequency of the driver continues to increase regardless of what happens to the ball, eventually reaching very high frequencies. Predict what will happen to the ball over time as the driver frequency slowly increases.

Answer:

(a) the input force is 36.56 N

(b) the input force is 37.49 N

Explanation:

Given;

density of hydraulic oil, ρ =  8.53 x 10² kg/m³

radius of plunger, r₁ = 0.135 m

radius of piston, r₂ = 5.43 x 10⁻³ m

Part (a) The input force needed to support 22600-N weight, when the bottom surfaces of the piston and plunger are at the same level;

[tex]P =\frac{F}{A}[/tex]

Where;

P is pressure

F is force

A is circular area = πr²

[tex]\frac{F_1}{A_1} =\frac{F_2}{A_2} \\\\F_2 = \frac{F_1*A_2}{A_1} =\frac{F_1* \pi r_2^2}{\pi r_1^2} = \frac{F_1* r_2^2}{ r_1^2} \\\\F_2 = \frac{22600*(5.43*10^{-3})^2 }{(0.135)^2}\\\\F_2 = 36.56 \ N[/tex]

Part (b) The input force needed to support 22600-N weight, when the  bottom surface of the output plunger is 1.20 m above that of the input plunger

[tex]P_2 = P_1 + \rho gh[/tex]

But, F = PA  and  A = πr²

[tex]F_2 = F_1(\frac{A_2}{A_1} ) + \rho gh*A_2\\\\F_2 = F_1(\frac{r_2^2}{r_1^2} )+\rho gh(\pi r_2^2)\\\\F_2 = 22600(\frac{5.43*10^{-3}}{0.135})^2 \ + 853*9.8*1.2*\pi (5.43*10^{-3})^2\\\\F_2=36.56 + 0.93\\\\F_2 = 37.49 \ N[/tex]

The solution of this problem involves the use of Pascal's principle and a concept known as hydrostatic pressure.

First, let's identify the given parameters:
- The density (ρ) of the hydraulic oil is 8.53 x 10ˆ2 kg/m³
- The radius of the input piston is 5.43 x 10ˆ-3 m
- The radius of the output plunger is 0.135 m
- The total weight (W) being lifted is 22600 N
- The acceleration due to gravity (g) is approximately 9.81 m/s²
- The height difference (Δh) between the pistons is 1.2 m

We will use these in our calculations.

We begin by determining the areas of the input piston and the output plunger using the formula for the area of a circle A = πr². We denote the area of the input piston as Ain and the area of the output plunger as Aout.

Let's now focus on when the pistons are at the same level.
Part (a) requires us to find the input force (F) needed to support the weight of the car and output plunger. This is governed by Pascal's principle, which states that for an incompressible, non-viscous fluid in a hydraulic system, pressure is transmitted undiminished throughout the fluid and acts with equal force on all areas. Using Pascal's principle, the force required on the input piston is equal to the weight divided by the ratio of the areas. F = W * (Ain / Aout). After performing the calculation, we find that F equivales to approximately 36.562893827160494 N.

Next, let's turn to when the bottom surface of the output plunger is 1.2 m above the input piston.
Part (b) of the problem asks us to calculate the input force needed in this scenario. We must consider not only Pascal's principle but the additional hydrostatic pressure due to the height difference between the pistons. Firstly, we calculate the hydrostatic pressure difference (ΔP): ΔP = ρ * g * Δh. We then add this pressure difference to the force required when pistons were at the same level. Remember that pressure is force divided by area, thus when we add pressure we need to multiply it by the area of the input piston to maintain the units consistent. F = F_same_level + ΔP * Ain. The result of this calculation yields an input force of approximately 37.49208673165364 N.

In conclusion, the input force required to support the specified weight when the bottom surfaces of the pistons are at the same level is about 36.56 N. This force increases to roughly 37.49 N when the output plunger is pushed 1.2 m above the input piston due to the added hydrostatic pressure.

https://brainly.com/question/20876092

#SPJ11

Answer:

Check the explanation

Explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer:

Kinetic energy depends on the mass of a body and the velocity it is travelling at

Explanation:

Referring to the equation of Kinetic Energy

EK = 0.5 m [tex]v^{2}[/tex]

We can see that Kinetic energy depends on the mass of a body and the velocity it is travelling at

Answer:

The amount of translational kinetic energy (from here on, the phrase kinetic energy will refer to translational kinetic energy) that an object has depends upon two variables: the mass (m) of the object and the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object.

Answer:

7350 J

Explanation:

Gravitational Potential Energy: This is defined as the energy possessed by a body due to it's position in the gravitational field. The S.I unit is Joules(J).

Applying,

E.p = mgh..................... Equation 1

Where E.p = Gravitational potential Energy, m = mass of the object, h = height of the object above the surface of the earth, g = acceleration due to gravity.

Given: m = 2.5 kg, h = 300 m

Constant: g = 9.8 m/s²

Substitute these values into equation 1

E.p = 2.5(300)(9.8)

E.p = 7350 J.

The initial speed of the bullet was determined by utilizing the principles of conservation of energy and momentum. The final velocity of the bullet and bob was first determined from the given height and the known conversion of kinetic to potential energy. This final velocity was then input into the conservation of momentum equation to find the initial speed of the bullet.

The ballistic pendulum is a classic example of a problem in physics which can be solved either by using the principles of work and energy or the principles of impulse and momentum. For this problem, we will utilize conservation of momentum. We know that the momentum before the collision is equal to the momentum after the collision.

Therefore, we can create the following equation: (m1×v1) + (m2×v2) = (m1+m2)×V, where m1 and v1 represent the mass and velocity of the bullet, m2 and v2 represent the mass and velocity of the block, and V is the final velocity of the bullet-block system. We know that the block was initially at rest, hence v2 = 0.

After the bob reaches maximum height, there's no kinetic energy (because the speed is zero), so all that original kinetic energy has been converted into potential energy, m×g×h, where m is the total mass (mass of bullet + mass of bob), g is the acceleration due to gravity, and h is the height the bob was raised. From here we can solve for V, then substitute back into the momentum equation to solve for v1, which represents the initial speed of the bullet.

https://brainly.com/question/35573030

#SPJ12

Using conservation of momentum and energy, the initial speed of an 8.0 g bullet fired into a 2.5 kg ballistic pendulum bob, which rises 6.0 cm, is approximately 339.9 m/s. The key steps involve converting units, applying conservation laws, and solving for the initial speed. Therefore, the bullet's speed is determined to be 339.9 m/s.

For solving this problem, we will use the principle of conservation of momentum and the principle of conservation of energy.

Step-by-Step Solution

Convert the masses into common units:

mass of bullet, [tex]m_{bullet[/tex] = 8.0 g = 0.008 kg

mass of pendulum bob = 2.5 kg.

Convert the rise height into meters:

h = 6.0 cm = 0.06 m.

Determine the final velocity of the combined bullet and pendulum system at the lowest point (right after the collision) using energy conservation:

At maximum height, all kinetic energy is converted to potential energy:

mgh = 0.5 (M + m) v²

Using v = √(2gh) since M includes the bullet:

v = √(2 * 9.8 m/s² * 0.06 m)

v = √(1.176)

v ≈ 1.084 m/s

Use conservation of momentum to find the initial speed of the bullet:

Initial momentum = [tex]m_{bullet[/tex] * [tex]v_{bullet[/tex]

Final momentum = (M + m) * v = (2.5 kg + 0.008 kg) * 1.084 m/s

So, p = (2.508 kg) * 1.084 m/s

p = 2.719 kg·m/s

Initial speed of the bullet:

[tex]v_{bullet[/tex] = p / [tex]m_{bullet[/tex]

[tex]v_{bullet[/tex] = 2.719 kg·m/s / 0.008 kg

[tex]v_{bullet[/tex] ≈ 339.9 m/s

Therefore, the initial speed of the bullet is approximately 339.9 m/s.

Given Information:

Current due to Lightning bolt = I₁ = 20 kA

Current of household = I₂ = 10 A

Distance = r₁ = 4.9 m

Distance = r₂ = 4.9 cm = 0.049 m

Required Information:

a) Magnetic field due Lightning bolt = B₁ = ?

b) Magnetic field due to household current = B₂ = ?

Answer:

a) Magnetic field due Lightning bolt = B₁ = 8.16×10⁻⁴ T

b) Magnetic field due to household current = B₂ = 4.08×10⁻⁵ T

B₁ = 20B₂

Explanation:

The magnetic field produced in a long straight wire carrying a current (I) at distance r is given by  

B = μ₀I/2πr  

Where μ₀ is the permeability of free space and its value is 4π×10⁻⁷

a) The magnetic field produced due to the lightning bolt current is

B₁ = μ₀I₁/2πr₁

B₁ = (4π×10⁻⁷*20,000)/2π*4.9

B₁ = 0.000816

B₁ = 8.16×10⁻⁴ T

Therefore, the strength of magnetic field due to the lightning bolt current is 8.16×10⁻⁴ T

b) The magnetic field produced due to the household current is

B₂ = μ₀I₂/2πr₂

B₂ = (4π×10⁻⁷*10)/2π*0.049

B₂ = 0.00004081

B₂ = 4.08×10⁻⁵ T

Therefore, the strength of magnetic field due to the household current is 4.08×10⁻⁵ T

The ratio of magnetic field produced by the lightning bolt current to the magnetic field produced by the household current is

B₁/B₂ = 8.16×10⁻⁴/4.08×10⁻⁵

B₁/B₂ = 20

B₁ = 20B₂

Which means that the magnetic field produced by the lightning bolt current is 20 time greater than the magnetic field produced by the household current.

a) The magnetic field due Lightning bolt  will be 8.16×10⁻⁴ T

b)The magnetic field due to household current will be 4.08×10⁻⁵ T

It is the type of field where the magnetic force is obtained. With the help of a magnetic field. The magnetic force is obtained it is the field felt around a moving electric charge.

The number of magnetic flux lines on a unit area passing perpendicular to the given line direction is known as induced magnetic field strength .it is denoted by B.

a) The magnetic field due Lightning bolt  will be 8.16×10⁻⁴ T

The magnetic field produced in a long straight wire carrying a current (I) at distance r is given by  

B = μ₀I/2πr  

Where μ₀ is the permeability of free space and its value is 4π×10⁻⁷

[tex]\rm B_1= \frac{\mu_0i_1}{2 \pi r} \\\\ \rm B_1= \frac{4 \pi \times 10^{-7} \times 20,00}{2 \times 3.14 4.9} \\\\ \rm B_1= 8.16 \times 10^{-4} \ T[/tex]

b) Magnetic field due to household current will be 4.08×10⁻⁵ T

[tex]\rm B_2= \frac{\mu_0i_2}{2 \pi r} \\\\ \rm B_2= \frac{4 \pi \times 10^{-7} \times 10}{2 \times 3.14 0.049} \\\\ \rm B_2= 4.08\times 10^{-5} \ T[/tex]

Hence the magnetic field due to household current will be 4.08×10⁻⁵ T

The magnetic field created by lightning bolt current divided by the magnetic field produced by home electricity equals

[tex]\rm \frac{B_1}{B_2} = \rm \frac{8.16 \times 10^{-4}}{4.08 c\times 10^{-5}} \\\\ \rm \frac{B_1}{B_2} = 20 \\\\[/tex]

That is, the magnetic field created by a lightning bolt current is 20 times stronger than the magnetic field produced by a home current.

Hence the magnetic field due to the Lightning bolt will be 8.16×10⁻⁴and the magnetic field due to household current will be 4.08×10⁻⁵ T.

To learn more about the magnetic field refer to the link;

https://brainly.com/question/19542022

To find the initial momentum of an alpha particle, we can use the equation: momentum = mass x velocity. The mass of an alpha particle is approximately 4 atomic mass units (amu). The velocity can be determined by considering the initial kinetic energy of the alpha particle.

The initial momentum of an alpha particle can be calculated using the equation:

momentum = mass x velocity

The mass of an alpha particle is approximately 4 atomic mass units (amu). The velocity of the alpha particle can be determined by considering its initial kinetic energy. Since the alpha particle is shot directly at a resting heavy nucleus, we can assume that its initial kinetic energy is equal to the energy of the system.

Using the equation:

kinetic energy = (1/2) x mass x velocity^2

we can solve for velocity. Then, using the calculated velocity, we can find the momentum of the alpha particle.

https://brainly.com/question/14863785

#SPJ3

Answer:

1, 2, and 5

Explanation:

Answer:

1, 2 and 5

Explanation:

Answer:

The uncertainty the  in position is  [tex]\delta s = 0.4051 m[/tex]

Explanation:

From the question we are  told

   The planck's constant is [tex]h = 0.70 \ J \cdot s[/tex]

  The mass of the baseball is  [tex]m = 0.55kg[/tex]

   The velocity of the baseball [tex]v_b = 22 m/s[/tex]

    The uncertainty in [tex]\delta v = 0.5 m/s[/tex]

Generally the uncertainty of  momentum is  

        [tex]\delta p = m \delta v[/tex]

 substituting values

        [tex]\delta p = 0.275 \ kg m/s[/tex]

The uncertainty position is mathematically represented as

             [tex]\delta s = \frac{h}{2 \p \delta p }[/tex]

 substituting values  

           [tex]\delta s = \frac{0.70}{2 * 3.142 * 0.275 }[/tex]

           [tex]\delta s = 0.4051 m[/tex]

Answer:

1.333 cm/s

Explanation:

The formula for the volume of the cube V in term of its edge s is:

[tex]V = s^3[/tex]

By using chain rule we have the following equation between the rate of change of the volume and the rate of change of the edge:

[tex]\frac{dV}{dt} = \frac{dV}{ds}\frac{ds}{dt}[/tex]

[tex]100 = \frac{d(s^3)}{ds}\frac{ds}{dt}[/tex]

[tex]100 = 3s^2\frac{ds}{dt}[/tex]

[tex]\frac{ds}{dt} = \frac{100}{3s^2}[/tex]

We can substitute s = 5 cm:

[tex]\frac{ds}{dt} = \frac{100}{3*5^2} = 100 / 75 = 1.333 cm/s[/tex]

Answer:density

Explanation:

At the bottom, deep bodies of water always measure [tex]4^{\circ}C[/tex] because at that temperature water has it highest density .

In water bodies like lake warm water rises up due to convection and at higher depths there is cold water, which is found to be at highest density of water.

When water molecules acquired heat energy  it become widely spread at the same volume and thus posses low density but at low temperature water molecule occupy less space therefore posses maximum density at [tex]4^{\circ}C[/tex]

Answer:

The third force  = [tex]-(26.0 \, N \, \hat{i} + 12.00 \, N \, \hat{j})[/tex]

Explanation:

Here we note that, the formula for the resultant force is as follows;

[tex]\Sigma F = \Sigma F_x + \Sigma F_y[/tex]

Also

∑F = m×a

Where:

[tex]F_x[/tex] = Force components in the x direction

[tex]F_y[/tex] = Force components in the y direction

∑F = Resultant force vector

m = Mass of the object

a = Acceleration vector ob the object =

[tex]a = 8.00 \, m/s^2 \, \hat{i} + 6.00 \, m/s^2 \, \hat{j}[/tex]

[tex]F_1 = 30.0 \, N \, \hat{i} + 16.0 \, N \, \hat{j}[/tex]

[tex]F_2 = 12.0 \, N \, \hat{i} + 8.00 \, N \, \hat{j}[/tex]

Therefore, since ∑F = m×a, we have;

[tex]\Sigma F = 2 kg \times (8.00 \, m/s^2 \, \hat{i} + 6.00 \, m/s^2 \, \hat{j})[/tex]

[tex]\Sigma F = (16.00 \, m/s^2 \, \hat{i} + 12.00 \, m/s^2 \, \hat{j})[/tex]

Hence from [tex]\Sigma F = \Sigma F_x + \Sigma F_y[/tex], we have;

[tex]F_{x1} + F_{x2} + F_{x3} = 16[/tex]

That is 30 + 12 + [tex]F_{x3}[/tex] = 16

∴  [tex]F_{x3}[/tex] = 16 - (30 + 12) = -26

Similarly,

[tex]F_{y1} + F_{y2} + F_{y3} = 12[/tex]

Therefore,  [tex]F_{y3}[/tex] = 12 - (16 + 8) = -12

Hence, [tex]F_3 = -26.0 \, N \, \hat{i} - 12.00 \, N \, \hat{j} = -(26.0 \, N \, \hat{i} + 12.00 \, N \, \hat{j})[/tex]

The third force, [tex]F_3, = -(26.0 \, N \, \hat{i} + 12.00 \, N \, \hat{j})[/tex]

The third force applied on the object calculated using Newton's second law provides a magnitude of (-26.00 N î - 12.00 N ĵ).

The subject of this problem is Newton's second law (F=ma), where F is the total force, m is the mass of the object, and a is acceleration. Each of these elements (i, j) represent a vector quantity with both a magnitude and a direction, and in this case, they represent different directions in two-dimensional space. The total acceleration of the object is a vector sum of these accelerations, as is the total force. Therefore, you can calculate the third force by subtracting the first two forces from the total force (which is found by multiplying mass and acceleration).  

Total Force (F) = m*a = (2 kg)*(8.00m/s² î + 6.00m/s² ĵ) = 16.00 N î + 12.00 N ĵ.

We know two forces, F1 = 30.00 N î + 16.00 N ĵ and F2 = 12.00 N î + 8.00 N ĵ. Adding them, we get F1 + F2 =  42.00 N î + 24.00 N ĵ.

The third Force (F3) is the total force (F) subtracted from (F1 + F2), thus, F3 = F - (F1 + F2) = (-26.00 N î - 12.00 N ĵ).

https://brainly.com/question/13447525

#SPJ3

Answer:

Force of friction is (-30 N).

Explanation:

The force applied on the  box across the floor is 30 N.

The force of gravity is (-8 N) and the the normal force is 8 N.

It is based on Newton's third law of motion. Newton's third law of motion states that the force acting on object 1 to object 2 is equal in magnitude of the force from object 2 to 1 but in opposite direction.

Here there is force of 30 N is applied in horizontal direction. The frictional force act in opposite direction. So, the force of friction is -30 N so that box across the floor.

Answer:

Vertex: Point where the principal axis and mirror meet

Focal point: Point we are reflected light converges or appears to diverge

Focal length: distance from the center of a mirror to the focal point

Principal axis: line that runs to the center of curvature to a mirror

Center of curvature: sensor of spherical mirror from which a curved mirror was cut

Explanation:

Just did the assignment on Edge.

A spherical mirror is a mirror which has the shape of a piece cut out of a spherical surface. There are two types of spherical mirrors: concave, and convex.

A spherical mirror is a mirror which has the shape of a piece cut out of a spherical surface. There are two types of spherical mirrors: concave, and convex. These are illustrated in.

The most commonly occurring examples of concave mirrors are shaving mirrors and makeup mirrors.

As is well-known, these types of mirrors magnify objects placed close to them. The most commonly occurring examples of convex mirrors are the passenger-side wing mirrors of cars.

These types of mirrors have wider fields of view than equivalent flat mirrors, but objects which appear in them generally look smaller

The answers to the given questions are:

Vertex: Point where the principal axis and mirror meet

Focal point: Point we are reflected light converges or appears to diverge

Focal length: distance from the centre of a mirror to the focal point

Principal axis: line that runs to the centre of curvature of a mirror

Center of curvature: sensor of spherical mirror from which a curved mirror was cut

To know more about Spherical mirrors follow

https://brainly.com/question/7512320

Answer:

(D) Decrease in width of 2.18 x [tex]10^{-6[/tex]m

Explanation:

Given:

force 'F'= 60,000 N

elastic modulus 'E' = 207 GPa => 2.07 x  [tex]10^{11[/tex]N/m²

cross section area ' [tex]A_{0}[/tex]'= 20 mm x 40 mm => 800mm² =>8 x [tex]10^{-4}[/tex] m²

∈z = б/E => (F/ [tex]A_{0}[/tex])/E => F/ [tex]A_{0}[/tex]E

∈z = 60,000/(8 x [tex]10^{-4}[/tex] x 2.07 x  [tex]10^{11[/tex])

∈z =3.62 x  [tex]10^{-4}[/tex]

Lateral strain is given by,

∈x= -v∈z => -(0.30)(3.62 x  [tex]10^{-4}[/tex])

∈x=1.09  x  [tex]10^{-4}[/tex]

Next is to calculate the change in width

ΔW= Wo x ∈x =>20 x 1.09  x  [tex]10^{-4}[/tex]

ΔW= -2.18 x  [tex]10^{-6[/tex] m

Therefore, the correct option is 'D'

The steel specimen, when pulled in tension, will experience a decrease in width. This decrement is calculated to be about 1.75*10^-7 m, closest to option (D) decrease in width of 2.18  10−6 m.

The change in the width of a steel specimen being pulled in tension can be found using the formula for strain in the lateral direction = -Poisson's ratio * (stress/Young's modulus). Here, the stress (force/area) is 60,000N/(20mm*40mm), the Young's modulus is 207 GPa, and the Poisson's ratio is 0.30. Plugging these values in, we get a lateral strain of -8.74*10^-6. The change in width, which is this lateral strain times the original width (20mm), will thus be a decrease of about 1.75*10^-4 mm, or 1.75*10^-7 m. Amongst the given options, this is closest to (D) decrease in width of 2.18  10−6 m.

https://brainly.com/question/31577326

#SPJ3

Answer:

(a) 64.6 kg/ms

(b) 4088.61 N

Explanation:

(a)

I = mΔv.................. Equation 1

Where I = impulse acting on the ball, Δv = change in velocity.

But,

Δv = v-u.............. Equation 2

Where v = final velocity, u = initial velocity.

Substitute equation 2 into equation 1

I = m(v-u).................. Equation 3

Assuming: upwards to be positive

Given: m = 1.9 kg, v = 9 m/s, u = -25 m/s (downward)

Substitute into equation 3

I = 1.9[9-(25)]

I = 1.9(9+25)

I = 1.9(34)

I = 64.6 kgm/s.

(b)

F = I/t................... Equation 4

Where F = Average force on the floor from the ball, t =  time of contact of the floor with the ball.

Given: I = 64.6 kgm/s, t = 0.0158 s

Substitute into equation 4

F = 64.6/0.0158

F = 4088.61 N

Answer:

A) Impulse = 64.6 N.s

B) Force = 4088.6 N

Explanation:

We are given;

Mass of ball;m = 1.9 kg

Initial velocity of ball;u = -25 m/s (negative value because ball was drop downward)

Final velocity of ball;v = 9 m/s

From Newton's second law of motion, we know that;

Impulse = Change in momentum

Thus;

Impulse = final momentum - initial momentum = mv - mu

Thus;

Impulse = m(v - u)

Plugging in the relevant values, we have;

Impulse = 1.9(9 - (-25)

Impulse = 1.9(9 + 25)

Impulse = 1.9(34)

Impulse = 64.6 N.s

B) As said earlier,

impulse = 64.6 N.s

Now, we are looking for the magnitude of the average force.

Now, Impulse is also expressed as Force x time.

Thus,

Force x time = 64.6 N.s

We are given time as 0.0158 s

Thus, making Force the subject of the formula, we now have;

Force = 64.6/0.0158

Force = 4088.6 N

Answer:

The acceleration of its center of mass is  

The frictional force is  [tex]f = 21.65 \ N[/tex]

Explanation:

From the question we are told that

      The mass of the ball is [tex]m = 17 kg[/tex]

     The radius of the ball is [tex]r = 50cm = \frac{50}{100} = 0.5m[/tex]

     the angle with the horizontal is [tex]\theta = 19 ^ o[/tex]

    The of the ball at the base is  [tex]v = 5.0 \ m/s[/tex]

This setup is shown on the first uploaded image

looking at the diagram we see that the force acting on the ball can be mathematically evaluated as

       [tex]mg sin \theta -f = ma[/tex]

Where f is the frictional force

The torque on the ball is mathematically represented as

      [tex]\tau = f * r[/tex]

This torque can also be mathematically represented as

       [tex]\tau = I \alpha[/tex]

where I is the moment of inertia of the ball which is mathematically represented as

              [tex]I = \frac{2}{3} m r^2[/tex]

While [tex]\alpha[/tex]  is the angular acceleration which is mathematically represented as

          [tex]\alpha = \frac{a}{r}[/tex]

So   [tex]\tau = \frac{2}{3} m r^2 * \frac{a}{r}[/tex]

Equating the both formula for torque

        [tex]f * r = \frac{2}{3} m r^2 * \frac{a}{r }[/tex]

  =>  [tex]f = \frac{2}{3} ma[/tex]

Substituting this for f in the above equation

      [tex]mg sin \theta = ma + \frac{2}{3} ma[/tex]

      [tex]g sin \theta = \frac{5}{3} a[/tex]

     [tex]a = \frac{3}{5} * g * sin \theta \alpha[/tex]

Substituting values

     [tex]a = 1.91 m/s^2[/tex]          

    Now substituting into the equation frictional force equation

             [tex]f = \frac{2}{3} * 17 * 1.91[/tex]

             [tex]f = 21.65 \ N[/tex]

Answer:

[tex]a=-1.92 m/s^{2}[/tex]

[tex]F_{f}=-21.76 N[/tex]

Explanation:

We can use the definition of the torque:

[tex]\tau=I\alpha[/tex]

When:

Now, torque is the product of the friction force times the radius.

[tex]F_{f}*R=\frac{2}{3}mR^{2}*\frac{a}{R}[/tex]

[tex]F_{f}=\frac{2}{3}ma[/tex] (1)

Now, let's analyze the force acting over the sphere using the Newton's second law.

[tex]F=ma[/tex]

[tex]-mgsin(\theta)-F_{f}=ma[/tex] (2)  

Let's put F(f) of the equation (1) into the equation (2):

[tex]-mgsin(\theta)-\frac{2}{3}ma=ma[/tex]

[tex]a=-\frac{3}{5}gsin(\theta)[/tex]

[tex]a=-\frac{3}{5}*9.81*sin(19)[/tex]

[tex]a=-1.92 m/s^{2}[/tex]

Hence: [tex]F_{f}=\frac{2}{3}ma=\frac{2}{3}*17*(-1.92)[/tex]

[tex]F_{f}=-21.76 N[/tex]

I hope it helps you!  

Answer:

Explanation:4meters

Work=10J

Force=2.5N

Distance=work ➗ force

Distance=10 ➗ 2.5

Distance=4meter

Final answer:

Given that the work done on a book was 10 J and the force required to move the book was 2.5 N, we use the formula Work = Force x Distance to find that the book was moved a distance of 4 meters.

Explanation:

The question asks to calculate the distance a book was moved given that the work done on the book was 10 J and the force required to move the book was 2.5 N.

To find the distance, we can use the formula for work, which is:

Work (W) = Force (F) * Distance (d)

From the formula, we can solve for distance (d) by rearranging the equation:

Distance (d) = Work (W) / Force (F)

Plugging in the given values:

d = 10 J / 2.5 N

This calculation yields:

d = 4 m

Therefore, the book was moved a distance of 4 meters.

Answer:

A. The force exerted by the truth on the car is the same size as the force exerted by the car on the truck: Ftruck = Fcar

Explanation:

Both vehicles will experience equal both opposite forces one on the other.

Answer:

The moment of inertia of the system decreases and the angular speed increases.

Explanation:

This very concept might not seem to be interesting at first, but in combination with the law of the conservation of angular momentum, it can be used to describe many fascinating physical phenomena and predict motion in a wide range of situations.

In other words, the moment of inertia for an object describes its resistance to angular acceleration, accounting for the distribution of mass around its axis of rotation.

Therefore, in the course of this action, it is said that the moment of inertia of the system decreases and the angular speed increases.

When Diego moves quickly to the center along a radius of the merry-go-round, the moment of inertia of the system increases and the angular speed decreases.

When Diego moves quickly to the center along a radius of the merry-go-round, the moment of inertia of the system increases and the angular speed decreases.

The moment of inertia is a measure of how resistant an object is to changes in its rotation. As Diego moves closer to the center, the distribution of mass in the system changes, resulting in an increase in moment of inertia.

According to the conservation of angular momentum, if the moment of inertia increases, the angular speed must decrease in order to maintain a constant angular momentum.

https://brainly.com/question/14190791

#SPJ3

Complete Question

An oil tanker has collided with a smaller vessel, resulting in an oil spill in a large, calm-water bay of the ocean. You are investigating the environmental effects of the accident and need to know the area of the spill. The tanker captain informs you that 18000 liters of oil have escaped and that the oil has an index of refraction of n = 1.1. The index of refraction of the ocean water is 1.33. From the deck of your ship you note that in the sunlight the oil slick appears to be blue. A spectroscope confirms that the dominant wavelength from the surface of the spill is 485 nm. Assuming a uniform thickness, what is the largest total area oil slick

Answer:

The  largest total area of the oil slick  [tex]A = 8.257 *10^{9} \ m^2[/tex]

Explanation:

From the question we are told that

     The volume of oil the escaped is  [tex]V = 18000 \ L[/tex]

    The refractive index of oil is [tex]n_o = 1.1[/tex]

     The refractive index of water is [tex]n_w = 1.33[/tex]

      The wavelength of the light  is [tex]\lambda = 485 \ nm = 485 * 10^{-9} \ m[/tex]

Generally the thickness of the oil for condition of constructive interference between the oil and the water is mathematically represented as

          [tex]d = m *\frac{\lambda}{2n_w}[/tex]

Where is the order of interference of the light and it value ranges from 1, 2, 3,...n

It is usually take as 1 unless stated otherwise by the question

substituting value

      [tex]d = 1 * \frac{485 *10^{-9}}{2 * 1.1}[/tex]    

      [tex]d = 218 nm[/tex]    

The are can be mathematically evaluated as

        [tex]A = \frac{V}{d}[/tex]

Substituting values

        [tex]A = \frac{18000}{218*10^{-8}}[/tex]

        [tex]A = 8.257 *10^{9} \ m^2[/tex]

Final answer:

Destructive interference between two waves occurs when their phase difference is [tex]\pi + 2\pi n[/tex], for any integer n, resulting in a minimized or zero resultant amplitude.

Explanation:

The full criterion for destructive interference between two waves is when the phase difference between the waves is [tex]\pi + 2\pi n[/tex] for any integer n. This occurs because two waves are exactly half a wavelength out of phase [tex]\pi[/tex] radians phase difference), resulting in the peaks of one wave aligning with the troughs of the other, canceling each other out. Unlike constructive interference, where the waves reinforce each other leading to increased amplitude, destructive interference leads to a decrease in amplitude, potentially down to zero in the case of perfect destructive interference with identical waves.

Expressed mathematically, for pure destructive interference, the phase difference must fulfill the condition: phase difference = [tex]\pi + 2\pi n[/tex] for any integer n. This means that the path length difference between the two waves must be an odd multiple of half the wavelength. The result is that at the points of destructive interference, the amplitude of the resultant wave is minimized or even becomes zero, eliminating the wave at that point.

Answer:

Either repel or attract.

Explanation:

Answer:

An electric motor

Explanation:

Answer:

the only part it doesn't flow through is an insulator

Explanation:

A conductor is material through which current flows easily; an insulator is material through which current does not flow easily.

Answer:

Length of the pipe = 53.125 cm

Explanation:

given data

harmonic frequency f1  = 800 Hz

harmonic frequency f2  = 1120 Hz

harmonic frequency f3  = 1440 Hz

solution

first we get here fundamental frequency that  is express as

2F = f2 - f1    ...............1

put here value

2F = 1120 - 800

F = 160 Hz

and

Wavelength is express as

Wavelength  = Speed ÷ Fundamental frequency    ................2

here speed of waves in air  = 340 m/s

so put here value

Wavelength  =340 ÷ 160

Wavelength   = 2.125 m

so

Length of the pipe will be

Length of the pipe = 0.25 × wavelength    ......................3

put here value

Length of the pipe = 0.25 × 2.125

Length of the pipe = 0.53125 m

Length of the pipe = 53.125 cm

Final answer:

The length of the pipe, which resonates at odd harmonics and has successive frequencies of 800 Hz, 1120 Hz, and 1440 Hz, is calculated to be approximately 32.2 centimeters. This calculation assumes that the pipe is closed at one end, and uses the relationship between the harmonics and the fundamental frequency.

Explanation:

The student is inquiring about determining the length of a pipe based on the frequencies of its successive harmonics. Since the successive harmonics are at 800 Hz, 1120 Hz, and 1440 Hz, and these frequencies are not direct multiples of each other, it suggests that we're dealing with a pipe that is closed at one end. Such pipes produce odd harmonics only. The given frequencies thus correspond to the fundamental (first harmonic), the third harmonic, and the fifth harmonic, respectively.

The frequency of the nth harmonic in a pipe closed at one end is given by:

fn = n(f1), where n is an odd integer and f1 is the fundamental frequency, which in this case is 800 Hz. So, the third harmonic would be 3(800 Hz) = 2400 Hz, which is incorrect given our second frequency is 1120 Hz. The provided frequencies imply that 800 Hz is, in fact, the third harmonic (800 Hz = 3f1). Hence, the fundamental frequency (f1) is 800 Hz / 3 = 266.67 Hz.

The wavelength (λ1) of the fundamental frequency in a tube closed at one end is given by λ1 = 4L. Using the formula for frequency (
f = v / λ), where v is the velocity of sound in air (approximately 343 m/s), we can calculate the length of the pipe by rearranging it to L = v / (4f1).

Therefore, L = 343 m/s / (4 * 266.67 Hz) = 0.322 meters or 32.2 cm.

Answer:

t = 3.38 s

Explanation:

We have,

Initial speed of the ball that leaves the student's hand is 16 m/s

Initially, the hand is 1.90 m above the ground.

It is required to find the time for which the ball in the air before it hits the ground. We can use the equation of kinematics as :

[tex]y_f=y_i+ut+\dfrac{1}{2}at^2[/tex]

Here, [tex]y_f=-1.9\ m, y_i=0[/tex] and a=-g

The equation become:

[tex]-1.9=16t-\dfrac{1}{2}\times 9.8t^2[/tex]

After rearranging we get the above equation as :

[tex]4.9t^2-16t-1.9=0[/tex]

It is a quadratic equation, we need to find the value of t. On solving the above equation, we get :

t = -0.115 s and t = 3.38 s (ignore t = -0.115 s )

So, the ball is in air for 3.38 seconds before it hits the ground.

Answer:the object is not accelerating

Explanation:

There object is not accelerating since there's no increase in velocity

Final answer:

Based on the descriptions of graphical data, we can conclude that the object has negative acceleration because its velocity is decreasing over time while it is moving in the positive direction, or its negative velocity is increasing over time. Also, since the object is moving in the negative direction, it experiences a negative displacement.

Explanation:

The question asks about the motion of an object based on different graphical representations. To determine the nature of this motion, we can analyze the provided diagrams. In this case, we have descriptions of how the velocity changes over time, which allows us to infer acceleration, and acceleration is defined as the change in velocity over time. According to the information, the object experiences a decrease in positive velocity, which indicates a negative acceleration, as acceleration is in the opposite direction to the velocity. Furthermore, it is mentioned that the object has a negative velocity which increases in magnitude, coherently resulting in negative acceleration as well.

Acceleration is a vector quantity, meaning it has both direction and magnitude. Since we are discussing a coordinate system where to the right is considered positive, any acceleration towards the left will be considered negative. The graphs that indicate an object having a constant negative velocity also imply that the object has negative displacement over the time period, because it's moving in the negative direction of the coordinate system.

Answer:

The speed of the clay immediately before the impact is 91.23 m/s

Explanation:

Given;

mass of clay, m₁ = 12g = 0.012 kg

mass of wooden block, m₂ = 100g = 0.1 kg

initial velocity of the wooden block, u₂ = 0

distance moved by the wooden block, d = 7.5 m

coefficient of friction, μk = 0.65

Apply the principle of conservation of linear momentum;

Total momentum before collision = Total momentum after collision

m₁u₁ + m₂u₂ = v(m₁ +m₂)

where;

u₁ is the initial velocity of the clay immediately before the impact

v is the common velocity of clay-block system after impact

u₂ = 0

m₁u₁ = v(m₁ +m₂)

[tex]U_1 = \frac{(m_1 + m_2)V}{m_1}[/tex] ------- equ. (i)

Apply the principle of conservation of energy after the impact

ΔK + ΔU = 0

where;

ΔK is change in kinetic energy

ΔU is change in internal energy of the system due to frictional force

[tex](K_f -K_i) + (F_k*d) = 0\\\\-K_i +F_k*d = 0\\\\K_i = F_k*d \\\\\frac{1}{2} (m_1+m_2)v_i^2 = \mu_k (m_1 +m_2)gd\\\\\frac{1}{2}v_i^2 = \mu_kgd\\\\v_i^2 = 2 \mu_kgd\\\\v_i = \sqrt{2 \mu_kgd}[/tex]

[tex]v_i[/tex] is the common velocity of the clay-block system immediately after the impact, which is equal to V in equation (i)

[tex]U_1 = \frac{(m_1+m_2)V}{m_1} = \frac{(m_1+m_2)v_i}{m_1}\\\\U_1 = \frac{m_1+m_2}{m_1}(\sqrt{2 \mu_kgd})\\\\U_1 = \frac{0.012+0.1}{0.012}(\sqrt{2 *0.65*9.8*7.5})\\\\U_1 = 9.3333(9.77497)\\\\U_1 = 91.23 \ m/s[/tex]

Therefore, the speed of the clay immediately before the impact is 91.23 m/s

Answer:all of the above

Explanation:

because thoughts relate to your emotions and your behaviors reflect to your emotions

Mental health is a reflection of one's thoughts, emotions, and behaviors. Positive thinking, managed emotions and constructive behaviors contribute to a healthy mental state.

Your mental health is indeed a reflection of your thoughts, emotions and behaviors. Accumulative thoughts and feelings can shape our mental well-being to a great extent. Similarly, our behaviors, influenced by these thoughts and feelings, can either nurture or deteriorate our mental health. A balance in all three – positive thinking, managing emotions and constructive behaviors lead to a healthy mental state.

https://brainly.com/question/33043544

#SPJ6

Answer:B

Explanation:

Power=p

Voltage=v

Resistance=r

Voltage for both:110v

For 60 watts bulb:

Resistance=v^2/p

Resistance=110^2/60

Resistance=(110x110)/60

Resistance=12100/60

Resistance=201.7 ohms

Current=power/voltage

Current=60/110

Current=0.55 amperes

For 100watts bulb:

Resistance=v^2/p

Resistance=110^2/100

Resistance=(110 x 110)/100

Resistance=(12100)/100

Resistance =121 ohms

Current=power/voltage

Current=100/110

Current=0.91

The 60W bulb has greater resistance and smaller current than the 100W bulb, based on calculations from the power, voltage and Ohm's Law.

In the case of light bulbs, power (P) is given by the formula P = IV, where I is the current and V is the voltage. Bulb A is rated at 60W and Bulb B at 100W, both functioning at a voltage (V) of 110V. To find the current (I) for each bulb, you would divide the power (P) by the voltage (V). This shows that Bulb B, with a higher wattage, has a greater current.

The resistance (R) of the bulbs can be found using Ohm's Law, which states R = V/I. This shows that Bulb A, with a smaller current, has a greater resistance.

Therefore, option B-'The 60W bulb has a greater resistance and smaller current than the 100 W bulb' is the correct statement.

https://brainly.com/question/33719176

#SPJ2