PHYSICS · Multi-part · CBSE · Physics · Work and Energy · Work and Energy
Problem
Two identical blocks, P and Q, each of mass 1.0 kg, are released from rest at the top of two different frictional ramps of equal vertical height 1.2 m. Ramp 1 (for block P) is short and steep; Ramp 2 (for block Q) is twice as long and less steep. For each block, a student constructs an energy bar chart at three positions: the top, halfway down, and the bottom.
For both blocks:
• At the top: only a gravitational potential energy bar of height 12 relative units is drawn.
Additional information from experimental measurements:
• At the halfway point on Ramp 1, block P has lost 2 J of mechanical energy to thermal energy due to friction.
• At the halfway point on Ramp 2, block Q has lost 4 J of mechanical energy to thermal energy due to friction.
• By the time each block reaches the bottom, block P has lost 4 J total to thermal energy, whereas block Q has lost 8 J total to thermal energy.
Assume no other energy transfers occur.
(a) For block P, draw or clearly describe the complete set of energy bars (gravitational potential, kinetic, and thermal) at the halfway point and at the bottom. Use consistent relative units where the original gravitational potential energy bar is 12 units tall.
(b) Repeat part (a) for block Q.
(c) Determine which block reaches the bottom with the greater speed. Justify your answer quantitatively.
(d) Explain how the differing shapes and lengths of the two ramps account for the differences in the thermal energy bars you described.