Question

1. When does force do work
a. Give two examples in which a force acts on an object, but the work done by the force is zero
2. If a person does 50; of work in moving a 300kg box over a 10m distance on a horizontal surface what is the maximum force required?
b. How much work is done when a force of 30N moves an object a distance of 3cm?

Answer 1

1. **When does force do work?**
Work is done by a force when there is displacement of the object in the direction of the force. Mathematically, work (W) is defined as:
\[ W = F \cdot d \cdot \cos(\theta) \]
Where:
- \( W \) is the work done,
- \( F \) is the magnitude of the force,
- \( d \) is the displacement,
- \( \theta \) is the angle between the force and the direction of motion.

**Examples where work done is zero:**
- **Example 1:** A person is pushing against a wall with a force but the wall does not move. Here, the force is applied, but displacement is zero, leading to zero work done.
- **Example 2:** An object is being carried horizontally at a constant height while a gravitational force acts on it vertically downward. Since the displacement is horizontal and the gravitational force is vertical (\( \theta = 90^\circ\)), the work done by gravity on the object is zero.

2. **If a person does 50 J of work in moving a 300 kg box over a 10 m distance on a horizontal surface, what is the maximum force required?**
- Given:
- Work done (W) = 50 J
- Distance (d) = 10 m

Using the work formula:
\[
W = F \cdot d
\]
Rearranging for force (F), we have:
\[
F = \frac{W}{d} = \frac{50\, J}{10\, m} = 5\, N
\]

Thus, the maximum force required is 5 N.

3. **How much work is done when a force of 30 N moves an object a distance of 3 cm?**
- Given:
- Force (F) = 30 N
- Distance (d) = 3 cm = 0.03 m (converting cm to meters)

Using the work formula:
\[
W = F \cdot d = 30\, N \times 0.03\, m = 0.9\, J
\]

Therefore, the work done is 0.9 Joules.