A roller coaster starts from rest at the top of a hill. What is the speed of the cart at the bottom of the 25-meter height location, if frictional work provided -5,506 J of energy throughout the path taken? The mass of the car and people is 198 kg.

Question

High School

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Answer :

Pawar675 Pawar675 · Answer 1 · 2024-08-15T07:55:25-04:00

The speed of the roller coaster at the bottom of the 25-meter height location hill is 29.53 m/s.

To determine the speed of the roller coaster at the bottom of the hill, you need to use the conservation of mechanical energy formula.

The formula is given as follows; KEi + PEi + Wnc = KEf + PEf

Where KEi is the initial kinetic energy,

PEi is the initial potential energy,

Wnc is the work done by non-conservative forces,

KEf is the final kinetic energy, and PEf is the final potential energy.

Since the roller coaster starts from rest at the top of the hill, its initial kinetic energy is zero (KEi = 0).

Thus, the conservation of mechanical energy formula can be rewritten as follows; PEi + Wnc = KEf + PEf

Solving for KEf, we get; KEf = PEi + Wnc - PEf

Substituting the values given; PEi = mgh = 198 kg × 9.8 m/s² × 25 m = 48,705 J

PEf = 0

Wnc = -5,506 J

KEf = 48,705 J - 5,506 J - 0KEf = 43,199 J

Since KE = 1/2mv², we can find the final velocity of the roller coaster as follows;

KEf = 1/2mv²v² = 2KEf / mv² = 2(43,199 J) / 198 kgv² = 873.68v = √873.68v = 29.53 m/s

Therefore, the speed of the roller coaster at the bottom of the hill is 29.53 m/s.

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