Question that I dont know how to answer

[shadow1010]

Hi Guys,
we were given this question, and I have no idea where to start.

A car is coasting without friction toward a hill with height 'h' and ratius of the curvature is 'r'.
(a) what initial speed 'vo' will result in the car's wheels just losing contact with the roadway as the car crests the hill?
(b) what happens if the initial speed of the car is greater than the value found in part (a)?

I have figured out that there are no non-conservative forces acting on the car, so the work (conservative) is equal to the work (total) but I don't know where to go from there...any suggestions?

 

[Mindscrape]

So, how does the normal component look all along the hill? Is it the biggest at the top of the hill, is it the smallest? What forces are acting on the car as it goes up the hill? Why am I so concerned about the normal anyway?

You might want to break the problem (a) up into a couple problems, what velocity it needs at the top of the hill to fly off and then how that velocity relates to the initial one (you're energy thoughts for this part are good).

 

[ogb p]

I would approach this problem by first identifying the known variables and equations that can be used to solve for the unknown variables. In this case, the known variables are the height of the hill (h) and the radius of curvature (r). The unknown variables are the initial speed (vo) and the point at which the car's wheels lose contact with the roadway.

To solve for the initial speed, we can use the conservation of energy principle, which states that the total energy (kinetic + potential) of a system remains constant. In this case, the total energy at the bottom of the hill (where the car starts coasting) is equal to the total energy at the top of the hill (where the car's wheels just lose contact with the roadway).

The total energy at the bottom of the hill is equal to the kinetic energy, which is given by 1/2mv^2, where m is the mass of the car and v is the initial speed. The total energy at the top of the hill is equal to the potential energy, which is given by mgh, where g is the acceleration due to gravity.

Setting these two energies equal to each other, we can solve for the initial speed (vo) that will result in the car's wheels just losing contact with the roadway:

1/2mv^2 = mgh
v^2 = 2gh
v = √(2gh)

This is the answer to part (a) of the question.

For part (b), if the initial speed of the car is greater than the value found in part (a), the car will have enough kinetic energy to overcome the potential energy at the top of the hill. This means that the car will continue to move over the crest of the hill and will not lose contact with the roadway. However, depending on the initial speed and the steepness of the hill, the car may experience a decrease in speed due to friction and may eventually come to a stop or continue to coast at a slower speed.