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...

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.