Use the steps outlined above to find the magnitude of the acceleration a of a ch

Question

Use the steps outlined above to find the magnitude of the acceleration a of a chair and the magnitude of the normal force FN acting on the chair: Yusef pushes a chair of mass m = 45.0 kg across a carpeted floor with a force F p (the subscript 'p' here is lowercase and throughout the question) of magnitude Fp = 144 Ndirected at = 35.0 degrees below the horizontal (Figure 1) . The magnitude of the kinetic frictional force between the carpet and the chair is Fk = 89.0 N .

Part E

What is the magnitude of the acceleration a of the chair? What is the magnitude of the normal force FN acting on the chair?

Express your answers, separated by a comma, in meters per second squared and newtons to three significant figures.

Explanation / Answer

Hi.

To answer this question we have to draw a free body diagram over the chair. Through that method, we can know the relation between the forces:

In this case the x axis is put parallel to the floor and the y axis is put perpendicular to the x axis. In that event, the relation between the forces is:

x axis: Fp cos(35°) - Fk = ma

y axis: Fn = mg + Fp sin(35°)

The first equation can be used to find the value of the acceleration:

a = (1/m) (Fp cos(35°) - Fk) = (1/45 kg) [ (144 N)(0.819) - 89 N] = 0.643 m/s2

The second equation can be used to find the normal force:

Fn = (45 kg)(9.8 m/s2) + (144 N)(0.574) = 524 N

I hope it helps.

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