1) A roller coaster (398 kg) moves from A (3.82 m above the ground) to B (29.4 m above the ground). Two non-conservative forces are present: friction does -1.82 x 104 J of work on the car, and a chain mechanism does +5.49 x 10^4 J of work to help the car up a long climb. What is the change in the car's kinetic energy KEf - KEo from A to B?

Would I multiply both the distance and work done for both A and B and then subtract them?

Initial PE-friction+workadded=final PE+final KE

let point A be at Height=0, point B is then (+29.4-3.82)

0-1.82E4+5.49E4=mg(29.4-3.82)+final KE

solve for final KE

For the values of mg, m would be 398kg and g is 9.8 correct?

To find the change in the car's kinetic energy (KE) from point A to B, you need to consider the work done on the roller coaster.

First, let's calculate the gravitational potential energy (PE) at both points A and B.

PE = mgh

Where:
m = mass of the roller coaster = 398 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height above the ground

At point A:
PE_A = m * g * h_A = 398 kg * 9.8 m/s^2 * 3.82 m

At point B:
PE_B = m * g * h_B = 398 kg * 9.8 m/s^2 * 29.4 m

Next, let's calculate the work done by the friction force and the chain mechanism.

Work done by friction (W_friction) = -1.82 x 10^4 J (negative sign indicates work done against the motion of the roller coaster)

Work done by the chain mechanism (W_chain) = +5.49 x 10^4 J (positive sign indicates work done in favor of the motion of the roller coaster)

Now, we can calculate the change in potential energy (ΔPE) from A to B:

ΔPE = PE_B - PE_A

Finally, we can calculate the change in kinetic energy (ΔKE) using the work-energy theorem:

ΔKE = W_net = W_chain + W_friction

where W_net is the net work done on the roller coaster.

To calculate the change in kinetic energy, substitute the given values:

ΔKE = (5.49 x 10^4 J) + (-1.82 x 10^4 J)

Once you have calculated ΔKE, you can find the final kinetic energy (KE_f) and the initial kinetic energy (KE_o) using the formulas:

KE_f = KE_o + ΔKE

Therefore, the change in the car's kinetic energy from A to B is given by ΔKE.