Physics homework help...please!!?

Question

A car shoots up a ramp at 179m/s. The ramp is 400m long and is angled at 45 degrees. The coefficient of friction between the car and the ramp is 0.5. A) How fast is the car moving at the end of the ramp? B) How much time does it take to travel the length of the ramp? C) Imagine that the car starts up the ramp at a speed less than 179m/s. What is the minimum speed the car could have and still exit the ramp?

Thank you soooo much for helping me :-)!! I really appreciate it.

Answer 1

I assume the car enters the ramp at the velocity vi = 179 m/s It's kinetic energy there is .5*m*vi^2. Going up the ramp it will lose energy (velocity) from two sources: potential energy change due to its rise in elevation, and energy loss to friction. The potential energy change = m*g*∆h, where ∆h is the elevation change. This is L*sinø where L = length of ramp and ø is its angle to the ground. So the potential energy change is m*g*L*sinø. The energy lost to friction is F*L, where F is the frictional force. The frictional force is that component of the car's weight perpendicular to the slope of the ramp times the coefficient of friction µ. That would be µ*m*g*cosø, The kinetic energy the car has at the end of the ramp is its initial KE - potential energy loss - frictional loss, or

.5*m*vf^2 = .5*m*vi^2 - m*g*L*sinø - µ*m*g*cosø

The mass m appears in each term and cancels out leaving

.5*vf^2 = .5*vi^2 - g*L*sinø - µ*g*cosø

vf = √[vi^2 - 2*g*L*sinø - 2*µ*g*cosø]


The car's decelleration up the ramp is uniform (the forces slowing it down are constant). The average velocity is (vi + vf)/2. Distance = velocity * time, so time = distance/velocity. Then the time up the ramp is 2*L/(vi + vf).

Finally, the minimum speed is where the initial KE is exactly equal to the potential energy change plus the frictional energy loss. See the answer to the first part for those values.

Answer 2

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Answer 3

can u name the chapter please!?
ill answer afterwards coz i dont want u to get the answers rong!

Answer 4

Have you done any work on the problem at all?....where did you get stuck?

Answer 5

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