1.) A rope is wrapped around a sold cylinder of mass 4kg, radius= .2m and the ro

Question

1.) A rope is wrapped around a sold cylinder of mass 4kg, radius= .2m and the rope is pulled with a force of 40 N for one complete revolution, how much work is done by force?

b.) Using the information from the above question, assuming the cylinder starts at rest what is its angular velocity after going one revolution?

2.) If a wheel (hollow cylinder of radius = .5m and mass of 2 kg) is held in place and is rotating with a frequency of 3 rev/s, what is the kinetic energy of the wheel?

b.) If the above wheel is rotating at an angular velocity of 15 rad/s, a torque is applied to stop the wheel over an angular displacement of 45 radians, what is the magnitude of the applied torque?

3.) If a solid and a hollow sphere are at the top of a ramp and are let go at the same time, if both spheres have the same mass and radius, which sphere will get to the bottom of the ramp first?

4.) A solid sphere (mass is .5kg, radius is 5 cm) is on the top of a ramp that is 1 meter off the ground and starts from rest, how fast is it going when it reaches the bottom of the ramp?

b.) If the solid sphere in the above problem has a velocity of 2 m/s at the base of the ramp and as it rolls begins to slow down and stops after .5 meter, what is the magnitude of the frictional force that stops the ball?

5.) A girl (m girl = 50 kg) is sitting on the edge of a merry-go-round (assume a solid disk) at the p[lay ground, the merry-go-round (m mgr =250 kg, r mgr = 1.5 meters) is rotating with an angular velocity of 15 radians/sec, the girl gets up and walks tp the very center of the merry-go-round, what is the new angular velocity of the merry-go-round with the girl in the center?

6.) An un-stretched spring is hung vertical and then has a .20 kg mass attached, it stretches 12 cm to its equilibrium position, what is the spring constant and the natural frequency of the spring?

7.) A spring (k=240 N/m) is attached to a mass (m=.5 kg) on a horizontal, frictionless surface and oscillates about the equilibrium position. The spring is displaced 20 cm from the equilibrium position and released. What is the maximum velocity that the mass will experience?

Explanation / Answer

7)Given that mass m=0.5kg spring constant k=240N/m amplitude is A=0.20m the angular velocity is =k/m     =240/0.5     =21.908rad/s then the maximum velocity v=A    =(21.908)(0.20)     =4.381 m/s   

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