6. Two blocks are released from rest at the same height. Block A slides down a steeper ramp than Block B. Both ramps are frictionless. The blocks reach the same final height indicated by the lower dashed line. Block B weighs more than Block A.

a. Is the work done by the gravitational force on Block A (greater/less than/equal to) the work done by the gravitational force on Block B? Explain your reasoning.

b. Is the speed of Block A (greater/less than/equal to) the speed of Block B? Explain your reasoning.

c. Is the momentum of Block A (greater/less than/equal to) the momentum of Block B? Explain your reasoning.

a. the work done by the gravitational force on Block A is less than the work done by the gravitational force on Block B.

b. the speed of Block A is equal to the speed of Block B.

c. the momentum of Block A is less than the momentum of Block B.

Explanation:

a. The  work done by the gravitational force is equal to:

w = m*g*h

where m is mass, g is the standard gravitational acceleration and h is height. Given that both blocks are released from rest at the same height, then, the bigger the mass, the bigger the work done.

b. With ramps frictionless, the final speed of the blocs is:

v = √(2*g*h)

which is independent of the mass of the blocks.

c. The momentum is calculated as follows:

momentum = m*v

Given that both bocks has the same speed, then, the bigger the mass, the bigger the momentum.