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## Homework Statement

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

b.3.1*10^4 N

c.1.7*10^4 N

d. 980N

e.1.6*10^3

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 ?

## Homework Equations

E=(1/2)*k*x^2 + (1/2)*m*v^2 + mgh

## The Attempt at a Solution

1. So I wrote out energy equation:

Initial: E=mgh=1500*g*23

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 ??