Question

the pacman arcade game went out of order at fat maxs arcade. max is dragging it 5.00 meters across the ground and out of the store with a rope tied to the center of the game and pulls at a 45° angle. what is the force he exerts if he performs 3,500.0 joules of work? your answer should be rounded to three significant figures. do not include units in your answer. enter the answer

Explanation:

Step1: Recall the work formula

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

Step2: Solve for force \(F\)

We need to isolate \(F\) from the formula \(W = Fd\cos\theta\). Rearranging gives \(F=\frac{W}{d\cos\theta}\).
Given \(W = 3500.0\), \(d = 5.00\), and \(\theta = 45^{\circ}\), and \(\cos45^{\circ}=\frac{\sqrt{2}}{2}\approx0.707\).
Substitute the values: \(F=\frac{3500.0}{5.00\times0.707}\).
First calculate \(5.00\times0.707 = 3.535\).
Then \(F=\frac{3500.0}{3.535}\approx990\).

Answer:

990