Question

a force of 75 n at an angle of 15° to the direction of motion moves a chair 3 m. which change would result in more work being done on the chair?
using 60 n of force
moving the chair 2 m
increasing the angle to 20°
decreasing the angle to 10°

Explanation:

Step1: Recall the work formula

The formula for work done by a force is \(W = Fd\cos\theta\), where \(F\) is the force, \(d\) is the displacement, and \(\theta\) is the angle between the force and the displacement.

Step2: Analyze each option

• Option 1 (using 60 N of force): Original \(F = 75\ N\), new \(F = 60\ N\). Since \(W\) is directly proportional to \(F\) (when \(d\) and \(\cos\theta\) are constant), decreasing \(F\) will decrease \(W\).
• Option 2 (moving the chair 2 m): Original \(d = 3\ m\), new \(d = 2\ m\). Since \(W\) is directly proportional to \(d\) (when \(F\) and \(\cos\theta\) are constant), decreasing \(d\) will decrease \(W\).
• Option 3 (increasing the angle to \(20^\circ\)): The cosine function \(\cos\theta\) decreases as \(\theta\) increases (for \(\theta\) between \(0^\circ\) and \(90^\circ\)). So, increasing \(\theta\) from \(15^\circ\) to \(20^\circ\) will decrease \(\cos\theta\), thus decreasing \(W\) (since \(W\) is proportional to \(\cos\theta\) when \(F\) and \(d\) are constant).
• Option 4 (decreasing the angle to \(10^\circ\)): The cosine function \(\cos\theta\) increases as \(\theta\) decreases (for \(\theta\) between \(0^\circ\) and \(90^\circ\)). So, decreasing \(\theta\) from \(15^\circ\) to \(10^\circ\) will increase \(\cos\theta\), thus increasing \(W\) (since \(W\) is proportional to \(\cos\theta\) when \(F\) and \(d\) are constant).

Answer:

decreasing the angle to \(10^\circ\)