To solve the problem step by step, we will calculate the work done by conservative forces, all forces, and forces other than conservative forces using the given kinetic and potential energies.
### Given Data:
- Kinetic Energy at A, \( K_A = 50 \, J \)
- Potential Energy at A, \( U_A = -30 \, J \)
- Kinetic Energy at B, \( K_B = -10 \, J \)
- Potential Energy at B, \( U_B = 20 \, J \)
### Step 1: Work Done by Conservative Forces
The work done by conservative forces can be calculated using the change in potential energy:
\[
W_C = -\Delta U = U_A - U_B
\]
Substituting the values:
\[
W_C = -(-30 \, J - 20 \, J) = -(-30 - 20) = -(-50) = -50 \, J
\]
### Step 2: Work Done by All Forces
The work done by all forces is equal to the change in kinetic energy:
\[
W_{all} = \Delta K = K_B - K_A
\]
Substituting the values:
\[
W_{all} = -10 \, J - 50 \, J = -60 \, J
\]
### Step 3: Work Done by Forces Other Than Conservative Forces
The work done by non-conservative forces can be calculated using the total change in energy (kinetic + potential):
\[
W_{non-conservative} = (K_B + U_B) - (K_A + U_A)
\]
Substituting the values:
\[
W_{non-conservative} = (-10 \, J + 20 \, J) - (50 \, J - 30 \, J)
\]
Calculating:
\[
W_{non-conservative} = (10 \, J) - (20 \, J) = -10 \, J
\]
### Final Answers:
(a) Work done by conservative forces, \( W_C = -50 \, J \)
(b) Work done by all forces, \( W_{all} = -60 \, J \)
(c) Work done by forces other than conservative forces, \( W_{non-conservative} = -10 \, J \)
---
