Question

mass = 2.0 kg
mass = 1.3 kg
two boxes and their masses are shown. which of the following situations shows work being done?
a student is lifting the small box 0 5 m from the floor to a table.
a student is sitting in a chair and holding both boxes.
a student is holding the large box 1 m above the floor.
a student is standing and holding the small box

Explanation:

Step1: Recall the work formula

Work \(W = F\times d\times\cos\theta\), where \(F\) is the force, \(d\) is the displacement, and \(\theta\) is the angle between the force and the displacement. When \(\theta = 0^{\circ}\), \(W = Fd\) (since \(\cos0^{\circ}=1\)). The force \(F = mg\) (from Newton's second law \(F = ma\), here \(a = g\approx9.8\ m/s^{2}\) for an object near the Earth's surface).

Step2: Analyze each option

• Option 1: Lifting the small box

The student applies a force \(F = m_{small}g\) (upward) and the box has a displacement \(d = 0.5\ m\) (upward). \(\theta = 0^{\circ}\), so \(W=m_{small}g\times d\). Substituting \(m_{small}=1.3\ kg\), \(g = 9.8\ m/s^{2}\), \(d = 0.5\ m\), \(W=1.3\times9.8\times0.5=6.37\ J\). Work is done.

• Option 2: Sitting and holding both boxes

There is a force \(F=(m_{large}+m_{small})g\) (to counter - act gravity), but the displacement \(d = 0\). Using \(W = Fd\), \(W=(m_{large}+m_{small})g\times0 = 0\). No work is done.

• Option 3: Holding the large box above the floor

There is a force \(F = m_{large}g\) (to counter - act gravity), but the displacement \(d = 0\). Using \(W = Fd\), \(W=m_{large}g\times0=0\). No work is done.

• Option 4: Standing and holding the small box

There is a force \(F = m_{small}g\) (to counter - act gravity), but the displacement \(d = 0\). Using \(W = Fd\), \(W=m_{small}g\times0 = 0\). No work is done.

Answer:

A student is lifting the small box \(0.5\ m\) from the floor to a table.