Question Video: Work Done by an Applied Force | Nagwa Question Video: Work Done by an Applied Force | Nagwa

Question Video: Work Done by an Applied Force

A toy cart is pulled for 4.4 m in a straight line across a floor. The force applied to the cart has a magnitude of 17 N and is aligned at 28° above the horizontal. How much work does the applied force do?

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Video Transcript

A toy cart is pulled for 4.4 meters in a straight line across a floor. The force applied to the cart has a magnitude of 17 newtons and is aligned at 28 degrees above the horizontal. How much work does the applied force do?

If we draw a picture of this process, we have a cart being pulled along by an applied force, 𝐹, where the force is applied at an angle we’ve called 𝜃 above the horizontal. If we call motion to the right motion in the positive direction, we’re told that the cart is pulled 4.4 meters that way. We can call this 𝑑. We want to know the work done on the cart by this applied force, 𝐹.

To solve for this value, we can recall that work is not only equal to the dot product of force and displacement. But it’s also equal to the product of their magnitudes times the cosine of the angle between them. In our case, we know the force magnitude, 𝐹, as well as the magnitude of the displacement, 𝑑. We’re given the angle 𝜃 that separates displacement from force and so are ready to plug in and solve for 𝑊.

When we calculate this product, we find that, to two significant figures, 𝑊 is 66 newton meters or 66 joules. That’s how much work is done on the cart over this distance by the applied force.

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