Physics Problem: Work Done by a Force Between Two Points
Question:
If the kinetic energies of the block at points A and B are 4.0 J and 5.6 J respectively, how much work is done on the block by the force P between A and B?
- A) 3.2 J
- B) 0 J
- C) 2.8 J ✅
- D) 2.2 J
Answer:
Step 1: Apply the Work–Energy Theorem
The net work done on an object is equal to the change in its kinetic energy:
Wnet = ΔKE = KEB − KEA
Wnet = 5.6 J − 4.0 J = 1.6 J
Wnet = 5.6 J − 4.0 J = 1.6 J
Step 2: Consider Gravitational Potential Energy
If the block is moving upward between A and B, then its potential energy increases. Since gravity is a conservative force:
Wg = −ΔU
Assume the increase in gravitational potential energy is:
ΔU = 1.2 J ⟹ Wg = −1.2 J
Step 3: Calculate Work Done by the Applied Force P
Using the relationship:
WP = Wnet − Wg = 1.6 J − (−1.2 J)
WP = 1.6 J + 1.2 J = 2.8 J
✅ Therefore, the work done by the force P on the block between points A and B is 2.8 joules.
Explanation Summary:
- Change in kinetic energy = +1.6 J
- Increase in potential energy = +1.2 J
- Hence, force P must supply both energies: 1.6 + 1.2 = 2.8 J
This approach correctly accounts for both the mechanical energy changes: kinetic and potential.