2019 A/L Physics Past Paper · Question 09 (English Medium)

Weightlifting — the signs of the work done

A weightlifter lifts a weight vertically up (positive direction) with his hands. The signs of the work done by

( $a$ ) his hands on the weight,

( $b$ ) gravity on the weight, and

( $c$ ) the weight on his hands, respectively, are

(1) (a) +, (b) +, (c) +
(2) (a) +, (b) −, (c) +
(3) (a) +, (b) −, (c) −
(4) (a) −, (b) +, (c) −
(5) (a) −, (b) −, (c) +

Answer and explanation

Answer: (3) (a) +, (b) −, (c) −

What the question asks

We want: the sign of the work done by each of the three forces.

For each force, look at how the body it acts on moves.

Relevant theory

If the force is acting at an inclination to the displacement, then the work done is equal to the product of the component of the force in the direction of the displacement and the displacement.

When a body on the ground is raised from the ground to a higher level, a certain amount of work is done on it and this work is stored in it as energy.

Applying it to this question

Up is the positive direction.

The weight moves up.

The hands move up with it.

The three forces:

(a) The hands push the weight up.

(b) Gravity pulls the weight down. That force is $mg$ .

Reasoning and calculation

The rule for the sign:

$W = Fs\cos\theta$

Force and movement in the same direction: $\theta = 0°$ . So $W > 0$ .

Force and movement in opposite directions: $\theta = 180°$ . So $W < 0$ .

$+$

$W_a = F_h\,h\cos 0^\circ = +F_h h$

$−$

$W_b = mg\,h\cos 180^\circ = -mgh$

$W_c = F_h\,h\cos 180^\circ = -F_h h$

So the signs are: (a) +, (b) −, (c) −.

The hands give energy to the weight. It is stored as potential energy.

The hands lose that energy. That is why (c) is negative.

Reading the options

In the table, only row (3) reads (a) +, (b) −, (c) −.

Why the other options fail

This option says: (a) +, (b) +, (c) +.

But gravity and the push on the hands both point down, while the movement is up. So (b) and (c) are −.

So it is wrong.

This option says: (c) is +.

But the weight pushes the hands down, and the hands move up. So (c) is −.

This option says: (a) is − and (b) is +.

But the hands push up and the weight moves up. So (a) is +. Gravity pulls down. So (b) is −.

This option says: (a) is − and (c) is +.

But (a) is +, because the push and the movement are both up. (c) is −, because the push is down and the hands move up.

Checks

Does it make sense?

Lift the weight slowly. Then the hands push with $mg$ .

Take $m = 100$ kg and $h = 1$ m.

(a) $W = +1000$ J.

(b) $W = -1000$ J.

(a) and (b) add up to zero. So the speed does not change. The energy $mgh$ is stored as potential energy. That fits.

Conclusion

(a) The force and the movement are in the same direction. So +.

(b) They are opposite. So −.

So the answer is option (3).

Taking the work done by the weight on the hands as positive.

The force is down. The hands move up.

$\cos 180° = -1$

So the work is negative.

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