Question

A block of mass 2 kg is pulled at a constant speed with a taut rope along a frictionless plane that is inclined at \(30^\circ\). Find the work done by the tension in the rope in pulling it a distance 4 m along the inclined plane. (Acceleration due to gravity \(g = 10 \, \text{m/s}^2\))

• A. 40 J
• B. 20 J
• C. 68 J
• D. 136 J

Hint:

For constant speed on a frictionless incline, work done by tension equals component of weight along the incline multiplied by distance: \(W = mg \sin \theta \cdot d\).

Answer 1

The Correct Option is A

Step 1: Use energy conservation instead of finding the tension first.
Constant speed on a frictionless incline means kinetic energy does not change, so every bit of work the tension supplies is stored as gravitational potential energy as the block rises.

Step 2: Find the height gained.
Moving a distance $d = 4$ m along an incline of $30^\circ$, the vertical rise is
\[ h = d\sin\theta = 4 \times \sin 30^\circ = 4 \times 0.5 = 2\ \text{m} \]

Step 3: Equate the work done by the tension to the gain in potential energy.
\[ W = mgh = 2 \times 10 \times 2 \]

Step 4: Compute.
\[ W = 40\ \text{J} \]

Step 5: Conclusion.
Since nothing is lost to friction and the speed stays constant, this is exactly the work the tension performs:
\[ \boxed{40\ \text{J}} \]