# Motion of a Block with Three Forces

Motion of a Block with Three Forces

Three forces of magnitudes , , and are applied to a mass , initially at rest, at angles shown on the diagram. In this problem, you will determine the resultant (total) force vector from the combination of the three individual force vectors. All angles should be measured counterclockwise from the positive x axis (i.e., all angles are positive).

Remember to express arguments of trigonometric functions in radians, not degrees.

A. Calculate the magnitude of the total resultant force acting on the mass.

Express the magnitude of the resultant force in newtons to two significant figures.

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B. What angle does make with the positive x axis?

Express your answer in degrees to two significant figures.

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C. What is the magnitude of the mass's acceleration vector, ?

Express your answer to two significant figures.

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D. What is the direction of ? In other words, what angle does this vector make with respect to the positive x axis?

Express your answer in degrees to two significant figures.

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E. How far (in meters) will the mass move in 5.0 s?

Express the distance in meters to two significant figures.

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F. What is the magnitude of the velocity vector of the block at ?

Express your answer in meters per second to two significant figures.

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G. In what direction is the mass moving at time ? That is, what angle does the velocity vector make with respect to the positive x axis?

Express your answer in degrees to two significant figures.

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#### Solution Preview

Frx = F1cos(25 deg) + F2 cos(325 deg) + F3 cos(180 deg)

= 4*cos(25 deg) + 6*cos(325 deg) + 8*cos(180 deg)

= 3.625 + 4.915 - 8

= -0.54 N

Fry = F1sin(25 deg) + F2 sin(325 deg) + F3 sin(180 ...

#### Solution Summary

The expert examines the motion of a block with three forces