Question

which of the following processes requires the most work? * a person holds a 1 kg weight still with outstretched arms. a person lifts a 1 kg weight 1 m off the floor. a 10 kg ball is rolled across the floor at a constant speed for a distance of 10 m. a 10 kg weight rests on a table.

Explanation:

Step1: Recall work - formula

Work \(W = Fd\cos\theta\), where \(F\) is force, \(d\) is displacement and \(\theta\) is the angle between force and displacement. Also, \(F = mg\) (weight), \(m\) is mass and \(g= 9.8\ m/s^{2}\).

Step2: Analyze case 1 (weight on table)

The weight on the table has no displacement in the direction of the gravitational - force. So, \(W_1 = 0\) since \(d = 0\).

Step3: Analyze case 2 (rolling ball)

The force of gravity acts vertically downwards and the displacement of the ball is horizontal (\(\theta = 90^{\circ}\), \(\cos\theta=0\)). So, \(W_2 = Fd\cos90^{\circ}=0\).

Step4: Analyze case 3 (lifting weight)

\(m = 1\ kg\), \(g = 9.8\ m/s^{2}\), \(d = 1\ m\), \(\theta = 0^{\circ}\), \(\cos\theta = 1\). \(F=mg = 1\times9.8\ N\). Then \(W_3=Fd\cos\theta=1\times9.8\times1\times1 = 9.8\ J\).

Step5: Analyze case 4 (holding weight)

The weight is held still, so \(d = 0\). Then \(W_4 = 0\).

Answer:

A person lifts a 1 kg weight 1 m off the floor.