Work & Energy (CIE AS Physics)

The diagram shows a barrel of weight 2.5 × 10³ N on a frictionless slope inclined at 40° to the horizontal.

A force is applied to the barrel to move it up the slope at constant speed.

The force is parallel to the slope.

What is the work done in moving the barrel a distance of 6.0 m up the slope?

A.     7.2 × 10³ J               B.     2.5 × 10⁴ J              C.     1.1 × 10⁴ J               D.     9.6 × 10³ J

Answer: 

Step 1: List the known quantities

• Weight, F = 2.5 × 10³ N at 40°
  • It is helpful to use F for the force of weight since W is used for work done
• distance, d = 6.0 m

Step 2: State the work done equation

Step 3: Calculate the force in the direction of travel

• The force needed to push the barrel needs to overcome the component of the barrel's weight that is parallel to the slope
• Since the force is parallel to the slope, the component of weight needed is parallel to the slope

$F = W \times \sin \left(40\right)$

$F = 2.5\times {10}^3 \times \sin \left(40\right)$

$F = 1607 \mathrm{N}$

Step 4: Substitute the known values into the work done equation to calculate

$W = 1607 \times 6.0$

$W = 9.6\times {10}^3 \mathrm{J}$

• Therefore, the correct answer is D