Question

3 Force and acceleration (20 points) Two smooth rocks with equal mass sit on smooth ice, where friction is so little that we can ignore it. You apply a certain force, Fo, to one of the rocks, resulting in the rock accelerating at a rate 0.1 m/sec2. If the two rocks are tightly tied together by a string to make a single object with twice the mass of one rock, and you apply the same force Fo to one of the rocks, what is the acceleration? (Assume you push toward the center of the rocks, so you don't cause any spinning motion.) 4 Forces in equilibrium (10 points) Two 100N weights are attached to a spring scale as shown. What is the force reading on the spring scale? (Hint: in equilibrium, the forces at both ends of a rope are equal in magnitude; the same is true for the spring inside the scale). 00N

Answer 1

3) The force is

$F_o=ma=m\times 0.1$

When the mass is doubled but the force remains the same

$F_o=2mA$

Therefore

$2mA=m\times 0.1$

Hence the acceleration of 2 rocks tied together is

$A=0.1/2=0.05\,m/s^2$

4) Since the forces on the spring are in opposite direction, the total force experienced by the spring will add up.

Force reading on the scale is

$F=100+100=200\,N$