# Free body diagram help

1. Jan 24, 2009

### Lemon Mint

1. Probem
Suppose a couch with a mass of 75 kg was resting on a frictionless floor. Roy wants to move the couch to the other side of the room so he pushes it with a force of 30 N for 5.0 seconds.
a) Make a free body diagram of the couch.
b) Find the net force on the couch.
c) Find the couch's acceleration.
d) What velocity will the couch reach?

2. Relevant equations
Acceleration=force/mass

3. The attempt at a solution
a) Will this be applied force of 30N pointing right, normal force pointing up, and force of gravity down? In that case, what are the values for the normal and gravity force?
b) Depending on above. Once I know the values I will add them/subtract to find the net force.

2. Jan 24, 2009

### LowlyPion

Welcome to PF.

The normal forces cancel. But as you should know by now their magnitude is |m*g|.

Hence you have your applied force - horizontally.

What then is the acceleration that 30 N produces on 75 kg?

Armed with that it's simple kinematics isn't it?

3. Jan 24, 2009

### chrisk

The force applied to the couch is horizontal. It's your choice if it's pointing to the right or left. Yes, the normal force is pointing up and the gravitational force is pointing down. These two forces cancel each other so there's only a net force in the horizontal direction. There is no frictional force. Since

F=ma

the acceleration can be found. Use the kinematic equations for one dimensional motion to find the final velocity of the couch.

4. Jan 24, 2009

### Lemon Mint

Not simple for me. I'm only on my second week of basic high school physics and I've missed most of my course due to being sick.
So bear with me if I don't understand.

Why would the normal forces cancel out? How do you know that gravity the same as the support force?

5. Jan 24, 2009

### chrisk

OK. The reason the normal force, the force pushing up, and the gravitational force cancel out is because the couch is not accelerating in the vertical direction. If these two forces did not cancel out then the couch would begin moving in the vertical direction. You are probably sitting in a chair right now and the normal force is the chair pushing you up and gravity is pulling you down but you remain at rest. The magnitude of these two forces is equal to your weight and the two forces are in opposite directions so they cancel each other giving a net force of zero. If the chair breaks, the normal force reduces and the gravitational force stays the same and you fall. In this case, the net force is no longer zero.

6. Jan 24, 2009

### Lemon Mint

Got it. Thanks a lot chrisk!

So in that case, the net force is 30N (the horizontal push).
The acceleration is f=ma -> 30=75a -> a=.4
And the velocity that the couch will reach is .4 x 5 = 2

Correct?

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