Question

1. Suppose a torque T is generated by applying a force F to a wrench. The force is applied
some distance L from the bolt that the wrench is tightening. If the force applied is
reduced to a quarter of the original force, and the new torque generated is 3T, at what
distance from the bolt is this new force applied?



2. Two extended bodies, object 1 and object 2, are left to roll down an incline from an
initial height of 0.5m. One object has moment of inertia I1 = (1/2)MR^2, and the other
has moment of inertia I2 = (3/2)MR^2, where M and R are the objects’ masses and radii,
respectively.   
a. Which object reaches the bottom of the incline first?
b. What are the velocities of each object when they reach the bottom?



3. A mass m collides inelastically with a mass M. Mass m has an initial velocity v, and mass
M is at rest.   
a. Is momentum conserved?
b. Is kinetic energy conserved?
c. Calculate the final velocity of the composite system. You may give your answer in
the form of an algebraic equation (i.e. you don’t need to compute any numbers).

Answer 1

1.

First case,

T=F*d

Gives,

d=T/F…….(1)

Second case,

T1=F2*d2 ……….(2)

But, T1=3T and F2=F/4

Plug these values in eqn(2),

3T= F/4* d2

d2=(3T)/(F/4)

d2=12T/F

From eqn(1)

d2=12d

Thus, the distance from the bolt is 12 time the initial distance.