Question

A block enters a rough horizontal surface with a speed of \( 6 \, \text{ms}^{-1} \) at \( x = 1.5 \, \text{m} \) and leaves the rough horizontal surface with a speed of \( 4 \, \text{ms}^{-1} \) at \( x = 2.5 \, \text{m} \). If the retarding force acting on the block is \( F = -25x \, \text{N} \) (where \( F \) is in newton and \( x \) is in meter), then the mass of the block is:

• A. 2.5 kg
• B. 10 kg
• C. 5 kg
• D. 4 kg

Hint:

The work-energy principle links the net work done by forces on a body to its change in kinetic energy, allowing the determination of mass when forces and displacements are known.

Answer 1

The Correct Option is C

Step 1: Use Work–Energy theorem directly

Total work done by force equals change in kinetic energy:

W = \Delta KE

Step 2: Evaluate work using average force idea

Force varies as F = -25x from x = 1.5 to 2.5

Average force:

F_{avg} = -25 \times \frac{(1.5 + 2.5)}{2} = -25 \times 2 = -50 \, \text{N}

Displacement:

s = 2.5 - 1.5 = 1

Work done:

W = F_{avg} \cdot s = -50 \times 1 = -50 \, \text{J}

Step 3: Change in kinetic energy

\Delta KE = \frac{1}{2}m(4^2 - 6^2)

\Delta KE = \frac{1}{2}m(16 - 36) = -10m

Step 4: Equate

-10m = -50

m = 5 \, \text{kg}

Final Answer: 5 \, \text{kg}