Question

You and your bicycle have a combined mass of 80.0 kg. When you reach the base of a bridge, you are traveling along the road at 5.00 m/s. At the top of the bridge, you have climbed a vertical distance of 5.20 m and have slowed to 1.50 m/s. You can ignore work done by friction and any inefficiency in the bike or your legs.

(a) What is the total work done on you and your bicycle when you go from the base to the top of the bridge?
(b) How much work have you done with the force you apply to the pedals?

Answer 1

The total work done on a cyclist and bicycle when moving from the base of a bridge to the top can be calculated using the work-energy principle. This involves the change in kinetic energy and potential energy of the system. The work done by the force applied to the pedals is equivalent to the total work done on the cyclist and bicycle.

The correct answer is B.

Step-by-step explanation:

To find the total work done on you and your bicycle, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy plus the change in its potential energy. This can be represented by the equation W = ΔKE + ΔPE, where ΔKE is the change in kinetic energy, and ΔPE is the change in potential energy.

(a) We calculate the change in kinetic energy and potential energy as follows:

• Kinetic Energy at the base: KE1 = 1/2 (80.0 kg)(5.00 m/s)2
• Kinetic Energy at the top: KE2 = 1/2 (80.0 kg)(1.50 m/s)2
• Potential Energy at the base: PE1 = 0 J (as the vertical distance is zero)
• Potential Energy at the top: PE2 = (80.0 kg)(9.80 m/s2)(5.20 m)

The change in kinetic energy is KE2 - KE1 and the change in potential energy is PE2 - PE1.

The total work done is the sum of these changes:

W = (KE2 - KE1) + (PE2 - PE1)

(b) The work you have done with the force you apply to the pedals is the same as the total work done on you and the bicycle since there is no work done by other forces like friction.