Pre-Calculus, 9th edition
31

 PAGE: 610 SET: Exercises PROBLEM: 31

The weight of the piano is .

The angle of inclination is .

Draw the related diagram:

How many pounds of force must Timmy exert to hold the piano in position.

Find the magnitude of the force that is causing the piano to roll up.

A force with the same magnitude in the opposite direction of will keep the wagon from rolling down the ramp.

The force of gravity is orthogonal to the level ground, so we can represent the force of the piano due to gravity by the vector is .

Determine the vector projection of onto , which is the force parallel to the ramp.

The vector is

The vector projection of onto is .

.

The magnitude of is , so the magnitude of the force required to keep the wagon from rolling down the hill is .

Timmy exerts a force of to hold the piano in position.

Timmy exerts a force of to hold the piano in position.

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