Solving a Spring-Ladle Problem: Work Rate at Equilibrium and Beyond

[HobieDude16]

I don't understand how to start part b. Could someone please point me in the right direction? Thank you!

A 0.29 kg ladle sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (k = 435 N/m) whose other end is fixed. The ladle has a kinetic energy of 10 J as it passes through its equilibrium position (the point at which the spring force is zero).
(a) At what rate is the spring doing work on the ladle as the ladle passes through its equilibrium position?
0 W
(b) At what rate is the spring doing work on the ladle when the spring is compressed 0.10 m and the ladle is moving away from the equilibrium position?
W

 

[HallsofIvy]

I really don't see how you could do part (a) and then have no idea how to start part (b). HOw about showing us what you have done?

 

[HobieDude16]

what i did for part a was just pretty much assume, and get it right. i figured when the spring force is zero, spring work is zero at equillibrium? right? then i don't know how to start part b. that's what i HAVE done

 

[HobieDude16]

well, so far, 6 of us are stumped on this one... nobody even knows how to start it

 

[Fredrik]

I agree with you about (a). Zero force means zero work.

I assume that what they mean by the rate at which the spring is doing work on the ladle is the amount of work done per second. That means you will have to figure out what the velocity of the ladle is. To find the velocity, you must find the kinetic energy T, which of course satisfies E=T+V, where E is the total energy (which is known) and V is the potential energy. You should be able to figure out what V is if you know what the force is.