More practice questions

  1. Q4. A force F⃗\vec F of (3i^+4j^)(3\hat i + 4\hat j) N moves a particle through a displacement d⃗\vec d of (2i^−j^)(2\hat i - \hat j) m. Find the work done. Is it positive or negative?

    Show answerHide answer W=F⃗⋅d⃗=3(2)+4(−1)=2 J\begin{aligned} W &= \vec F \cdot \vec d \\ &= 3(2) + 4(-1) \\ &= 2\ \text{J} \end{aligned}

    It is positive, so the angle between the force and the displacement is less than 90°.

  2. Q5. A cyclist and cycle of total mass 80 kg ride 500 m up a road that rises 1 m for every 20 m along it. How much work does gravity do on them? Take g = 9.8 m s−2.

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    The road rises 1 m in 20 m, so the component of the weight along the road is mg/20, opposing the motion. Over 500 m its work is −(mg/20)(500), which is −mg × 25: the same as −mgh for the 25 m rise.

    Wg=−mgh=−80×9.8×25=−19 600 J\begin{aligned} W_g &= -mgh \\ &= -80 \times 9.8 \times 25 \\ &= -19\,600\ \text{J} \end{aligned}

  3. Q6. A porter carries a 20 kg suitcase on his head along a level platform for 50 m at a steady speed. How much work does he do on the suitcase? Explain.

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    None. The force he applies on the suitcase is upward, equal to its weight, while the suitcase moves horizontally. The force is at right angles to the displacement, so cos 90° = 0 and no work is done on it, though he does get tired.