- #1
Millenium
- 2
- 0
The question is An object of mass m is traveling on a horizontal surface. There is a coefficient of kinetic friction u between the object and the surface. The object has speed when it reaches x = 0 and encounters a spring. The object compresses the spring, stops, and then recoils and travels in the opposite direction. When the object reaches x = 0 on its return trip, it stops.
The question then asks me to find the spring constant k.
The answer to the problem has to be in terms of the following symbols:
u = coefficient of kinetic friction
m = mass of block
g = acceleration due to gravity
v = initial velocity of the block
I used conservation of energy
E(final) = E(initial) + W(nonconservative forces)
E(final) = 0 because the block is at rest (i think)
E(initial) if trying to find k could probably only be found if E(initial) = 1/2*k*x^2 right?
and then the W(nonconservative forces) = -m*g*u*x
then in order to find x I'd have to find how far the block would go with initial velocity v along the surface with u being the friction. So I'd get x = (v^2)/(2*u*g).
And then plugging everything back in and solving for k i get:
(4*g^2*m*u^2)/(v^2)
I figured that'd be the answer but when I put it into the online answer it says that its off by a multiplicative factor. Where did I go wrong?
The question then asks me to find the spring constant k.
The answer to the problem has to be in terms of the following symbols:
u = coefficient of kinetic friction
m = mass of block
g = acceleration due to gravity
v = initial velocity of the block
I used conservation of energy
E(final) = E(initial) + W(nonconservative forces)
E(final) = 0 because the block is at rest (i think)
E(initial) if trying to find k could probably only be found if E(initial) = 1/2*k*x^2 right?
and then the W(nonconservative forces) = -m*g*u*x
then in order to find x I'd have to find how far the block would go with initial velocity v along the surface with u being the friction. So I'd get x = (v^2)/(2*u*g).
And then plugging everything back in and solving for k i get:
(4*g^2*m*u^2)/(v^2)
I figured that'd be the answer but when I put it into the online answer it says that its off by a multiplicative factor. Where did I go wrong?