# The applied and friction forces of a particle

1. Apr 12, 2015

### Edd988

1. The problem statement, all variables and given/known data
A particle of mass 14kg, slides along a straight wire in a horizontal plane. The coefficient of dynamic friction u=0.6 The equation of the line of the wire is y=3√x so that the angle between the wire and the X-axis is 60 degrees.

The particle accelerates with a constant acceleration whose magnitude is a=2 At time t=3s the particle is at A. The acceleration is produced by an applied force P acting parallel to the X-axis.

(b) Show that the magnitude of P is P = 220.8 newtons

2. Relevant equations
F=ma
F=UR (U is coefficient of dynamic friction and R is R=mgcos(x))

3. The attempt at a solution

P-F=ma
F=UR
P=ma + F
F=0.6*mgcos(theta) = 41.202
P=14*2 + 41.202
P=69.202

2. Apr 13, 2015

### haruspex

A few problems there.
P and a are not in the same direction, so P-F=ma is wrong.
The wire is horizontal, so mg cos(theta) is wrong.
What are all the forces on the particle, and in what directions do they act?

3. Apr 13, 2015

### Edd988

The normal force acts perpendicular to the wire, the gravity force acts downward to the particle, the applied force will push the particle, and the friction force will act in the opposite way.
I though the plane was horizontal and the angle between the wire and the plane is 60 degree?

4. Apr 13, 2015

### ehild

The wire is also horizontal, it makes 60 degree angle with the x axis.

5. Apr 13, 2015

### jatin9953

I guess, the wire is at 60 degree from horizontal.

6. Apr 13, 2015

### haruspex

Right, but that leaves a range of possibilities for the direction.
Yes, but in which direction does P act in relation to (a) the horizontal plane and (b) the x axis (c) the wire?
Opposite to what exactly? I.e., which direction is the force of friction in relation to (a) the horizontal plane and (b) the x axis (c) the wire?

7. Apr 13, 2015

### haruspex

That's not what it says:

8. Apr 13, 2015

### jatin9953

I tried it, with conservation of energy and got the answer close to 208N

9. Apr 13, 2015

### haruspex

I get a rather larger result. The tricky part is calculating the normal force correctly.

10. Apr 13, 2015

### ehild

The result given in the problem is obtained if friction exist between the ground and the object only. The object slides along the wire, on the ground.

11. Apr 13, 2015

### haruspex

Hmm... there's nothing in the OP about a ground, and it sounds like the friction is between particle and wire. Edd, have you stated the problem exactly as given to you?