# A shopper in a supermarket pushes a cart with a force of 34 N directed at an angle of 23◦ downward from the horizontal. A shopper in a supermarket pushes a cart with a force of 34 N directed at...

A shopper in a supermarket pushes a cart with a force of 34 N directed at an angle of 23◦ downward from the horizontal.

A shopper in a supermarket pushes a cart with a force of 34 N directed at an angle of 23◦ downward from the horizontal.

Find the work done by the shopper on the cart as the shopper moves along a 51.6 m length of aisle.

Answer in units of J

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To solve this you need to recognize that because the force is being applied at an angle, part of the force is pushing vertically down on the cart and part of the force is pushing horizontally on the cart causing it to move forward.

You first need to determine the portion of the force that is being directed horizontally using the cosine function.

Construct a right triangle where the hypotenuse is the actual force of 34 N being applied. Cos 23 degrees = X/34N where X is the force horizontally and 34 N is the actual applied force.

Solving you get a horizontal force of 31.3 N.

Now work is the product of the force and the distance moved.

W = Fd

W = 31.3 N * 51.6m = 1614.90 J of work done.