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 28ยฐ 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, ๐น, where the force is applied at an angle weโve called ๐ above the horizontal. If we call motion to the right motion in the positive direction, weโre told that the cart is pulled 4.4 meters that way. We can call this ๐. We want to know the work done on the cart by this applied force, ๐น.

To solve for this value, we can recall that work is not only equal to the dot product of force and displacement. But itโ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, ๐น, as well as the magnitude of the displacement, ๐. Weโre given the angle ๐ that separates displacement from force and so are ready to plug in and solve for ๐.

When we calculate this product, we find that, to two significant figures, ๐ is 66 newton meters or 66 joules. Thatโs how much work is done on the cart over this distance by the applied force.

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