1. A roller coaster car of mass 1500kg starts a distance H=23m above the bottom of a loop 15m in diameter. If friction is negligible, the downward force the rails on the car when it is upside down at the top of the loop is:
a. 4.6*10^4 N
2.A block of mass m is pushed up against a spring, compressing it a distance x and the block is then released. The spring projects the block along a frictionless horizontal surface, giving the block a speed v. The same spring projects a second block of mass 4m, giving it a speed 3v. What distance was the spring compressed in the second case ?
E=(1/2)*k*x^2 + (1/2)*m*v^2 + mgh
The Attempt at a Solution
1. So I wrote out energy equation:
Final: E= (1/2)*m*v^2 + mgh = (1500*v^2/2)+ 1500*15*g
then I set them equal and get 23*g= (1/2)*v^2 + 15g then I solve for v^2= 16*g
F=mv^2/2 = 16*9.81*1500 / 7.5 = 31392 N then I chose b. However, I am wrong. can you guys help me identify where did I do wrong ?
2.I also did the same
Initial: E= k*x^2 /2
Final: E= m*v^2 /2
I set them equal and get k*x^2= m*v^2
I substitute 4m for mass and 3v for speed and get k*x^2 = 4m*9v^2
I solved for x= squroot (4*m*9*v^2/k)
My answer was wrong too. I think because it contains k and they don't give k in the givens. How can I fix it ??