The applied and friction forces of a particle

[Edd988]

Homework Statement

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

Homework Equations

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

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
[/B]

 

[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?

 

[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?

 

[ehild]

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?

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

 

[jatin9953]

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

 

[haruspex]

The normal force acts perpendicular to the wire

Right, but that leaves a range of possibilities for the direction.

the applied force will push the particle

Yes, but in which direction does P act in relation to (a) the horizontal plane and (b) the x-axis (c) the wire?

friction force will act in the opposite way

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?

 

[haruspex]

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

That's not what it says:

along a straight wire in a horizontal plane

 

[jatin9953]

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

 

[haruspex]

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

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

 

[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.

 

[haruspex]

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.

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?