Reading a Potential Energy graph

[Hyacinth42]

Homework Statement

Potential Energy Graph A conservative force F(x) acts on a 2.0 kg particle that moves along the x axis. The potential energy U(x) associated with F(x) is graphed in Fig. 10-46. When the particle is at x = 2.5 m, its velocity is -2.0 m/s. The "kinks" in the graph occur at (1, -2.8), (4, -17.2), and (8.5, -17.2); and the endpoint is at (15, -2).

Figure 10-46

(a) What are the magnitude and direction of F(x) at this position?

(b) Between what limits of x does the particle move?

(c) What is its speed at x = 7.0 m?

I have no idea how to interpret the graph, please help?

 

[LowlyPion]

Homework Statement

Potential Energy Graph A conservative force F(x) acts on a 2.0 kg particle that moves along the x axis. The potential energy U(x) associated with F(x) is graphed in Fig. 10-46. When the particle is at x = 2.5 m, its velocity is -2.0 m/s. The "kinks" in the graph occur at (1, -2.8), (4, -17.2), and (8.5, -17.2); and the endpoint is at (15, -2).

(a) What are the magnitude and direction of F(x) at this position?

(b) Between what limits of x does the particle move?

(c) What is its speed at x = 7.0 m?

I have no idea how to interpret the graph, please help?

Think in terms of the conservation of energy. As potential energy changes what does it change to or come from? (Hint: Kinetic Energy)

For your particle then, they give you how much Kinetic Energy the particle has at a certain point. Now they want to know what its range is within the range of the potential energy of the graph.

 

[Insomniac18]

I also have trouble with this problem. I really don't know where to go with it. I understand that F(x)=-dU(x)/dx, but that's really it. Any help would be appreciated.

The graph shows the potential energy, but how do I find the kinetic energy? And how does this help solve the problem? Maybe I'm missing something, but I don't see the relation of velocity to potential energy.

 

[LowlyPion]

I also have trouble with this problem. I really don't know where to go with it. I understand that F(x)=-dU(x)/dx, but that's really it. Any help would be appreciated.

The graph shows the potential energy, but how do I find the kinetic energy? And how does this help solve the problem? Maybe I'm missing something, but I don't see the relation of velocity to potential energy.

Welcome to PF.

I'm sure you've heard of the conservation of energy, and this is where it happens.

In the problem they give you mass and velocity hence you know Kinetic energy.

KE = ½m*v²

In this problem they also tell you by the graph what Potential energy is.

Hence you know what the Total energy is.

KE + PE = Constant

As you move in X then if the potential increases then you may be sure that the kinetic energy decreases and of course vice versa.