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
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.