Question

1. a skater moves across the ice a distance of 12 m before a constant frictional force of 15 n causes them to stop. if their initial speed is 2.2 m/s, determine the skaters mass. a. 2.8 kg b. 163 kg c. 74 kg d. 37 kg

Explanation:

Step1: Use work - energy theorem

The work - energy theorem states that \(W=\Delta K\). The work done by the frictional force \(W = Fd\cos\theta\). Since the frictional force \(F\) and the displacement \(d\) are in opposite directions (\(\theta = 180^{\circ}\), \(\cos\theta=- 1\)), \(W=-Fd\). The change in kinetic energy \(\Delta K=K_{f}-K_{i}\). The final kinetic energy \(K_{f} = 0\) (skater stops), and the initial kinetic energy \(K_{i}=\frac{1}{2}mv_{i}^{2}\). So, \(-Fd=0 - \frac{1}{2}mv_{i}^{2}\).

Step2: Solve for mass \(m\)

From \(-Fd=-\frac{1}{2}mv_{i}^{2}\), we can cancel out the negative signs. Then \(Fd=\frac{1}{2}mv_{i}^{2}\). Rearranging for \(m\), we get \(m=\frac{2Fd}{v_{i}^{2}}\).
Substitute \(F = 15\space N\), \(d = 12\space m\), and \(v_{i}=2.2\space m/s\) into the formula:

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Answer:

C. \(74\space kg\)