Help with a potential energy/oscillation problem

[Laughter]

Homework Statement

Hi, guys, i need help with part d pleasee D: I've attached the diagram they're referring to. The only thing that's strange is that this is the energy/work etc. unit...

4. Figure 2 shows a sketch the total potential energy U (in Joules) as a function of position x (in meters) for a particle A of mass mA = 1.0 kg.

(a) Estimate the force (in Newtons) experienced by the particle.
(b) Estimate the minimum velocity at which the particle should be projected in order for it to reach the
position x = 0. What direction should it be projected?
(c) If the particle were instead released from rest, what is its maximum displacement?
(d) Estimate the minimum time taken for the particle in part (c) to return to A.
(e) If a weak frictional force were acting on the particle in part

Homework Equations

not sure

The Attempt at a Solution

i've already converted the y-axis so it is in terms of height and not u, by dividing each term by mg so it shows me the height with respect to x, but for part d I am not sure how close of an estimate they want. i think something could be done with SHM, and that the acceleration felt by the particle is -gsinθ. Or approximate the curve to be semi circular around that point and use the length of the path traveled but i don't know exactly where to go with the ideas i have..

some help would be greatly appreciated!

 

[Spinnor]

When the particle reaches 6m you should be able to figure out the velocity at that point. The particle goes 8m in one round trip. Use these numbers for a minimum estimate.

Alternatively you know U = kx^2/2 , from the graph you can estimate k for the range x= 4 to 8m and you know ω = (k/m)^.5 = 2∏/period

 

[Laughter]

how would i do that? sorry we haven't done harmonic motion yet, would you mind explaining what the variables represent? how did you get that the round trip is 8m?

 

[haruspex]

From the PE/distance graph you can sketch a graph relating velocity to distance by taking the square root of the KE.
v = sqrt(2*KE/m) = sqrt(2*(U₀-U)/m)
If you plot y=1/v against against x then you can estimate the time taken to get from x₀ to x₁ by looking at the area under the graph between those values: dt = dx/v = y.dx