- #1
fysics4liefe
- 3
- 0
Homework Statement
A toy car of mass 0.300 kg is shot out of a compressed horizontal spring (A), and then travels around a loop-the-loop along a frictionless track. The spring has a spring constant k = 900 N/m, and 3.50 J of energy was stored in the spring by compressing it.
(1) How far was the spring compressed to store 3.5 J of energy in it?
(2) What is the speed of the car as it passes point B, which is 0.400 m above point A?
(3) How high above the original position does the car go before stopping (point C)?
(4) Suppose now that the track has some friction, and that it is observed that the car's height at point C is only 80% of the height it would reach in the absence of friction (i.e. in Question #3). How much energy did friction remove on the trip from A to C?
Homework Equations
KE = (1/2)mv2
PE = mgh
PES = (1/2)kx2
The Attempt at a Solution
(1) PE = (1/2)kx2, so 3.5 = (0.5)(900)x2. Solving for x, x = 0.088. So this is the distance the spring was compressed in order to store 3.5 J.
(2) To be honest, I have attempted this about 10 different ways, none of which were correct. I believe that mgh = (1/2)mv2 could be used in some way, but am not sure of how to use this, because I don't know what the maximum height would be. (1/2)mv12 = (1/2)mv22 + mgh could be useful as well, if either velocity was known. Perhaps the velocity can be figured from the amount of energy that was stored in the spring.
(3) & (4) Without knowing the answer to #2, it is difficult/impossible to even get started on these ones. Please advise. Thank you all in advance.