What is the work done when a force is applied at an angle of 90 degrees to the direction of movement?

What is the work done when a force is applied at an angle of 90 degrees to the direction of movement?

• A. It is maximized
• B. It is zero
• C. It is equal to the force times the distance
• D. It is equal to the force divided by the distance

Answer: (B)

When a force is applied at an angle of 90 degrees to the direction of movement, the work done is zero. Work is calculated using the formula: \[ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) \] where \( \theta \) is the angle between the force and the direction of movement. In this case, since the angle is 90 degrees, the cosine of 90 degrees is zero: \[ \cos(90^\circ) = 0 \] This means that the work done is: \[ \text{Work} = \text{Force} \times \text{Distance} \times 0 = 0 \] Thus, no work is done when the force is perpendicular to the direction of movement, as the force does not contribute to displacement in the direction of the force. This is a fundamental concept in physics, highlighting how the direction of force relative to movement is crucial in determining the work done.

When a force is applied at an angle of 90 degrees to the direction of movement, the work done is zero. Work is calculated using the formula:

[ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) ]

where ( \theta ) is the angle between the force and the direction of movement. In this case, since the angle is 90 degrees, the cosine of 90 degrees is zero:

[ \cos(90^\circ) = 0 ]

This means that the work done is:

[ \text{Work} = \text{Force} \times \text{Distance} \times 0 = 0 ]

Thus, no work is done when the force is perpendicular to the direction of movement, as the force does not contribute to displacement in the direction of the force. This is a fundamental concept in physics, highlighting how the direction of force relative to movement is crucial in determining the work done.