A 10.0 kg block is moving on horizontal floor with negligible friction. Class 9
A 10.0 kg block is moving on horizontal floor with negligible friction. Class 9
Question 1.
A 10.0 kg block is moving on horizontal floor with negligible friction. As shown in the Fig., a variable force is applied on the block in its direction of motion from its position at 0 m till 4 m. If the block had a kinetic energy of 180 J when it was at 0 m, find the block’s speed (i) at 0 m, and (ii) at 4 m. Does the block have negative acceleration in any portion of its motion?
Answer:
(i) Speed at 0 m: KE = 1/2 mv². 180 = 14 × 10 × v². v² = 36. v = 6 m s-1.
(ii) Work done by force = Area under force- displacement graph (Fig.):
- 0 to 2 m (triangle, force 0 to 50 N): Area = 1/2 × 2 × 50 = 50 J
- 2 to 3 m (rectangle, force = 50 N): Area = 1 × 50 = 50 J
- 3 to 4 m (triangle, force 50 to 0 N): Area = 1/2 × 1 × 50 = 25 J
- Total work done = 50 + 50 + 25 = 125 J
Final KE = 180 + 125 = 305 J. 1/2 × 10 × v² = 305 → v² = 61 → v = [latex]\sqrt {61}[/latex] ≈ 7.81 m s-1.
Negative acceleration: The applied force is always positive (in the direction of motion) and friction is negligible, so no negative acceleration occurs in any portion.