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To find: How many pounds of force must Timmy exert to hold the piano in position?
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Answer to Problem 31AYU
Solution:
lbs.
Explanation of Solution
Given:
Billy and Timmy are using a ramp to load furniture into a truck. While rolling a 250-pound piano up the ramp, they discover that the truck is too full of other furniture for the piano to fit. Timmy holds the piano in place on the ramp while Billy repositions other items to make room for it in the truck. If the angle of inclination of the ramp is .
Calculation:
Angles of and form the alternate angles, so they are equal.
We wish to find the magnitude of the force that is acting to cause the piano up the ramp. A force with the same magnitude in the opposite direction of will keep the piano in place on the ramp. The force of gravity is orthogonal to the level ground, so the force of the wagon due to gravity can be represented by the
Determine the vector projection of onto ,
The vector projection of onto is,
The magnitude of is pounds, so the magnitude of the force required to keep the piano up the ramp is pounds.
Chapter 9 Solutions
Precalculus
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