A girl and her bicycle have a total mass of 43.0 kg. At the top of the hill her speed is 5.0 m/s, and her speed doubles as she rides down the hill. The hill is 10.0 m high and 105 m long. How much kinetic energy and potential energy is lost to friction?Select one:a.2,602 Jb.2,502 Jc.2,064 Jd.4,752 Je.2,702 J
Question
A girl and her bicycle have a total mass of 43.0 kg. At the top of the hill her speed is 5.0 m/s, and her speed doubles as she rides down the hill. The hill is 10.0 m high and 105 m long. How much kinetic energy and potential energy is lost to friction?Select one:a.2,602 Jb.2,502 Jc.2,064 Jd.4,752 Je.2,702 J
Solution
First, let's calculate the initial kinetic energy (KE) and potential energy (PE) at the top of the hill.
The formula for kinetic energy is KE = 1/2 * m * v^2, where m is the mass and v is the velocity.
So, KE = 1/2 * 43.0 kg * (5.0 m/s)^2 = 537.5 J
The formula for potential energy is PE = m * g * h, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the height.
So, PE = 43.0 kg * 9.8 m/s^2 * 10.0 m = 4214 J
Now, let's calculate the final kinetic energy at the bottom of the hill. The speed doubles, so v = 2 * 5.0 m/s = 10.0 m/s.
So, KE = 1/2 * 43.0 kg * (10.0 m/s)^2 = 2150 J
The potential energy at the bottom of the hill is 0, because the height is 0.
The total initial energy (kinetic + potential) is 537.5 J + 4214 J = 4751.5 J
The total final energy (kinetic + potential) is 2150 J + 0 = 2150 J
The energy lost to friction is the initial energy minus the final energy, so 4751.5 J - 2150 J = 2601.5 J
So, the answer is approximately 2602 J, which is option a.
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