In the lab, we have a ramp. On it, there\'s a cart connected to a spring. Let it

Question

In the lab, we have a ramp. On it, there's a cart connected to a spring. Let it go, and it will travel a certain distance. Find the distance.

I'm trying to use the potential energies to find this.
So I found my K to be 3.34 by using weights and distance.

I set up my initial E (I guess?) as Spring potential energy and Gravitational energy.
1.2 k x^2 + mgh = 1.2 k x^2 + mgh
initial spe is 0, and final gpe is 0, so
mgh = 1.2 k x^2

so the initial mgh is the height from the table to the track, which is .17 m, and the mass of my car is .502 kg.
and so my mgh here is : .83
and thats equal to 1/2 k (3.34) x^2
so my x ends up being around 70cm.

Which is WRONG because I tested it, and the answer is around 30-40.

QUESTION: in the initial gravitational potential energy, do I need to put gravity as along the ramp? as in cos() * 9.8?
Because we I do this, the answer is .28 m.

?? Thanks so much

Explanation / Answer

x is the length of spring compressed from its natural length not the distance travelled by the cart. Initial energy = final energy P.E + sP.E + K.E = P.E + sP.E + K.E Initially, it is at rest, so K.E = 0 Finally, it is at ground level and there is no spring, so P.E = 0 and sP.E = 0 Therefore, P.E1 + sP.E1 = K.E2 From the V, you can find the d. d = v/t

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