Question

d. the horizontal component of the force of tension does zero work on the box.

1. a 3.2 kg snow shovel is pushed at an angle of 35° from the horizontal with a force of 62 n from rest. the shovel reaches a speed of 3.1 m/s. determine the distance the shovel travelled.

a. 0.10 m b. 0.30 m c. 0.61 m d. none of the above

Explanation:

Step1: Calculate the work done by the force

The work - energy theorem states that \(W=\Delta K\). The work done by the force \(F\) is \(W = Fd\cos\theta\), where \(F = 62\space N\), \(\theta=35^{\circ}\), and \(d\) is the distance we want to find. The initial kinetic energy \(K_{i}=0\) (starts from rest) and the final kinetic energy \(K_{f}=\frac{1}{2}mv^{2}\), with \(m = 3.2\space kg\) and \(v = 3.1\space m/s\).

So, \(Fd\cos\theta=\frac{1}{2}mv^{2}\)

Step2: Solve for \(d\)

We can re - arrange the formula \(d=\frac{mv^{2}}{2F\cos\theta}\)

Substitute the values: \(m = 3.2\space kg\), \(v = 3.1\space m/s\), \(F = 62\space N\), \(\cos\theta=\cos35^{\circ}\approx0.819\)

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Answer:

B. \(0.30\space m\)