- 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.
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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.
- Given:
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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.
- Given:
1 answer