A roller coaster with a mass of 500.0 kg starts from a height of 27.0 meters with a speed of 5.1 m/s. It descends to a height of 2.00 meters before it starts back up. Some energy is loss to the work due to friction. The speed at the bottom of the ramp is 22.0 m/s. How much energy was lost to friction?

KEtop + (m g h) = KEbottom + (friction loss)

I'm not getting any correct answers with this formula....I'm not sure what I'm doing wrong here

1/2(0.5)(5.1)^2 top
1/2(0.5)(22.0)^2 bottom

what?

how do I calculate friction?

To find the energy lost to friction, we first need to calculate the initial potential energy, the final kinetic energy, and the work done against friction.

1. Calculate the initial potential energy:
The initial potential energy (PE) is given by the formula PE = mgh, where m is the mass (500.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height (27.0 m).
PE = (500.0 kg) * (9.8 m/s^2) * (27.0 m)

2. Calculate the final kinetic energy:
The final kinetic energy (KE) is given by the formula KE = (1/2)mv^2, where m is the mass (500.0 kg) and v is the final velocity (22.0 m/s).
KE = (1/2) * (500.0 kg) * (22.0 m/s)^2

3. Calculate the work done against friction:
The work done against friction (W) can be found using the work-energy principle, which states that the work done on an object is equal to the change in its mechanical energy.
W = KE - PE

4. Calculate the energy lost to friction:
The energy lost to friction is equal to the negative amount of work done against friction.
Energy lost = -W

Now let's plug the values into the formulas to find the energy lost to friction:

PE = (500.0 kg) * (9.8 m/s^2) * (27.0 m)
KE = (1/2) * (500.0 kg) * (22.0 m/s)^2
W = KE - PE
Energy lost = -W

Simply calculate the value of PE, KE, W, and Energy lost using the formulas, and you will get the energy lost to friction.

KE top + PE top -energy lost to friction (L)=KE bottom + PE bottom

500*9.8*27 + 1/2(500)*5.1^2 =138802.5

500*9.8*2 + 1/2(500)*22^2 = 130800

138802.5-L=130800
138802.5=130800+ L
138802.5-130800=L
8002 J lost to friction