Question

several children are on a sled pulled by a four-wheeler across a level snow - covered field. the sled is moving at a constant speed of 9.50 m/s, and the tow rope (parallel to the ground) makes an angle of 35.0°, with respect to the velocity of the sled (see the figure below).
if the tension in the rope is 45.0 n, determine the work done (in j) on the sled by the tension in the rope in 11.0 s.

Explanation:

Step1: Calculate the displacement of the sled

The formula for displacement \(d = vt\), where \(v = 9.50\space m/s\) and \(t=11.0\space s\).

$$d=(9.50\space m/s)\times(11.0\space s)=104.5\space m$$

Step2: Calculate the work done by the tension

The formula for work \(W = Fd\cos\theta\), where \(F = 45.0\space N\), \(d = 104.5\space m\), and \(\theta = 35.0^{\circ}\).

$$W=(45.0\space N)\times(104.5\space m)\times\cos(35.0^{\circ})$$

$$W = 45\times104.5\times0.8192$$

$$W=45\times85.6$$

$$W = 3852\space J$$

Answer:

\(3852\space J\)