# Physics problem: Force and magnitudeA man cleaning his apartment pushes a vac-uum cleaner with a force of magnitude 42.8 N.The forcemakes an angle of 16.5◦ with the hor-izontal floor. The vacuum...

Physics problem: Force and magnitude

A man cleaning his apartment pushes a vac-

uum cleaner with a force of magnitude 42.8 N.

The forcemakes an angle of 16.5◦ with the hor-

izontal floor. The vacuum cleaner is pushed

2.62 m to the right along the floor.

Calculate the work done by the 42.8 N force.

Answer in units of J.

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### 1 Answer

It is given that the vacuum cleaner is pushed with a force of 42.8 N, and the direction of the force makes an angle of 16.5 degrees with the horizontal. This makes the vacuum cleaner move a distance of 2.62 m to the right along the floor.

We’ll first divide the force applied, into its horizontal and vertical components. The component of the force acting downwards is equal to 42.8*sin 16.5 = 12.15 N. The component of the force acting in the horizontal direction is equal to 42.8*cos 16.5 = 41.03 N.

Now the movement of the vacuum cleaner is in the direction of the horizontal component of the force applied. Work done is equal to the product of the force applied and the distance moved.

This gives the work done by the force as 41.03*2.62m = 107.5 J. There is no work done by the vertical component of the force.

**The required work done by the force is equal to 107.5 J.**