A roller coaster car of mass 1000kg is riding along a track from point A to point C. (point A is 75m high, B is 50m high and C is 100m high, so that there are a total of three hills.) the final velocity at point C is 10m/s

a) Assume no friction what is the speed of the car at the top of hill A?

intial = final
1/2mv_a^2 +mgh_a = 1/2mv_c^2 + mgh_c
1/2V_a^2 + 750 = 1050
V_a = 24.5 m/s

b) what is the max speed the car can achieve along the track?

What would be the equation for this part of the problem?

c) assume the car starts with the same speed as a) and there is friction present. The car does 50000J of work while the car moves from A to C, will the car still be able to ascend to the top of hill C? At what speed is the car at the top of C?

W= change in KE
and I got V_c = 26.5m/s

d) If the distance along the track from point A to point C is 200m what is the average magnitude of the force of friction between the track and the car?

I don't know how to find this part of the problem can you please help me?

cant you use the energy lost on the track (avgfrictionforce*distance) to find it? You know the starting and ending energies...

Intial PE+ initial KE= final PE+ final KE + frictionforce*total distance.

on b), use energy again.

a)You seem to be using g = 10 m/s^2 instead of the actual 9.8 m/s^2. If you are going to carry three significant figures, you should use a g that is that accurate. You also do not seem to have used h_c of 100 m in your g h calculation.

b)To get the highest speed, you need information on the lowest elevation. You have not provided that information.

c) To do this, you need the accurate starting velocity at A, but I am not sure you did part a) correctly to obtain that value

d) Divide the 50,000J work done (which I assume is frictional) by the distance travelled (200 m) to get the average force.

To find the max speed the car can achieve along the track (part b), we can use the law of conservation of energy. At the highest point (hill B), all of the car's potential energy is converted into kinetic energy.

Using the equation for conservation of mechanical energy:

mgh_a = 1/2mv_max^2 + mgh_max

Since we don't know the value of v_max, we need to rewrite the equation to solve for it.

Rearranging the equation, we get:

v_max = sqrt(2gh_a - 2gh_max)

Substituting the known values, we have:

v_max = sqrt(2 * 9.8 m/s^2 * 75 m - 2 * 9.8 m/s^2 * 50 m)

Simplifying, we find:

v_max = sqrt(1470) ≈ 38.3 m/s

Therefore, the maximum speed the car can achieve along the track is approximately 38.3 m/s.

Moving on to part c, where friction is present, we need to consider the work done by friction to determine if the car can still ascend to the top of hill C.

Given that the car does 50000 J of work, we can equate this to the change in kinetic energy (KE) of the car:

Work (W) = ΔKE

Since the work done by friction is negative (it opposes motion), the equation becomes:

W = -ΔKE

Substituting the given value:

-50000 J = 1/2mv_c^2 - 1/2mv_a^2

If we know the values of v_a (which was calculated in part a) and v_c (which is what we're trying to find), we can solve this equation.

Plugging in the known values:

-50000 J = 1/2 * 1000 kg * v_c^2 - 1/2 * 1000 kg * (24.5 m/s)^2

Simplifying:

-50000 J = 500 kg * (v_c^2 - 24.5 m/s)^2

Now, we can solve for v_c by rearranging the equation:

v_c^2 - 24.5 m/s = -100 J/kg

v_c^2 = 24.5 m/s - 100 J/kg

v_c^2 = 24.5 m/s - 100 m^2/s^2

v_c ≈ 26.5 m/s

Therefore, the car will still be able to ascend to the top of hill C, and its speed at the top of C is approximately 26.5 m/s.

Finally, for part d, to find the average magnitude of the force of friction between the track and the car, we'll use the work-energy theorem. The work done by friction is equal to the change in kinetic energy:

Work (W) = ΔKE

Since the car starts and stops at rest, the total work done by friction over the entire distance is also equal to the initial kinetic energy (KE_i):

W = KE_i

Given the work done (50000 J) and the distance (200 m), we can determine the average force of friction (F_friction) using the equation:

W = F_friction * d

Substituting the known values:

50000 J = F_friction * 200 m

Solving for F_friction:

F_friction = 50000 J / 200 m

F_friction = 250 N

Therefore, the average magnitude of the force of friction between the track and the car is 250 N.