Problem: An object with mass 3.0 kg slides down a slope with angle 15 degrees an

Question

Problem:

An object with mass 3.0 kg slides down a slope with angle 15 degrees and friction u= 0.1. which of the following are true:(may be one or several true alternatives)

1. No forces act on the object

2.There's a friction of 29.4 N acting on the object

3. There's a friction of 28.4 N acting on the object

4. There's a friction of 7.62 N acting on the object

5. There's a friction of 2.84 N acting on the object

6. The object is speeding up downward

7. The object is moving downward, but slowing down

I am told to use g=9.81

I calulate mg = 3.0 kg *9.81 = 29.43N

Than components of gravity force are: mgy = 29.43 *cos15 = 28.4N and mgx=mg*sin 15= 7.62 N

The normal force is equal to mgy=28.4N. The friction force R =u*N =0.1*28.4= 2.84

Since the the x component of gravity force is 7.6N.

So my answers are: number 5) Friction force = 2.84N and 6) The object is speeding up downwards since the x component of gravity is larger than the friction. Do I understand this correctly?

Explanation / Answer

We know that frictional force is given by:

F = mu N

N in the given case will be: N = m g cos(theta)

F = 0.1 x 3 x 9.81 x cos15 = 2.84 N

So the correct answers are:

(5) There's a friction of 2.84 N acting on the object

(6) The object is speeding up downward

Since the frictional force in Y direction is less than the force of gravity in y direction.

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