During a testing process, a worker in a factory mounts a bicycle wheel on a stat

Question

During a testing process, a worker in a factory mounts a bicycle wheel on a stationary stand and applies a tangential resistive force of 125 N to the tire's rim. The mass of the wheel is 1.90 kg and, for the purpose of this problem assume that all of this mass is on the outside radius of the wheel. The diameter of the wheel is 55.0 cm. A chain passes over a sprocket In order for the wheel to have an angular accelera that is concentric with the wheel and has a diameter of 9.00 cm. concentrated o 3.30 rad/s (increasing in speed from rest), what force must be applied to the chain? (Enter the magnitude only

Explanation / Answer

To determine the horizontal distance, we need to determine the sphere’s velocity at the bottom of the ramp. If we use conservation of potential and kinetic energy, the decrease of its potential energy will be equal to the increase of its kinetic energy.

PE = m * g * h = m * 9.8 * (1.75 – 1.38) = m * 3.626
Since the sphere is rolling without slipping, it has translational and rotational kinetic energy.
Translational = ½ * m * v^2

Rotational KE = ½ * I * ^2
I = ½ * m * r^2
= v/r, ^2 = v^2/r^2

Rotational KE = ½ * (½ * m * r^2) * v^2/r^2 = ¼ * m * v^2
Total KE = ¾ * m * v^2
Set this equal to the decrease of potential energy and solve for v.

¾ * m * v^2 = m * 5.782
v^2 = 4/3 * 3.626
v = (4/3 * 3.626)
This is approximately 2.1988 m/s. To determine the horizontal distance, we need to determine the time for the sphere to fall 1.38 meters. Use the following equation.

d = vi * t + ½ * a * t^2
vi is the initial vertical velocity, this is 0 m/s, a = 9.8 m/s^2

1.38 = ½ * 9.8 * t^ 2
t = (1.38/4.9)
This is approximately 0.5307 second.
Horizontal distance = (4/3 * 3.626) * (1.38/4.9)
This is approximately 1.167 meters.

To determine the number of revolutions, we need to determine the sphere’s angular velocity. Use the following equation. = v/r
= (4/3 * 3.626)/0.08
This is approximately 27.485 rad/s. As the sphere rotates one time, it rotates an angle of 2 radians. To determine the number of radians, multiply the angular velocity by the time.

N = (4/3 * 3.626)/0.08 * (1.38/4.9) = 14.586.
To determine the number of revolutions, divide by 2 .
N = 14.586 ÷ (2 )
This is approximately 2.32 revolutions

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