Aa particular bicycle is 25% effificent in converting the energy of a cyclist to mechanical energy (that is, she puts in four times as much energy as she gets out). if a cyclist is travelling along a pathway at a constant speed of 5.8 m/s for 1 h, and the aveage resistance is 22 N, how much mass does she lose assuming 1 kg is lost for each 2.9 x 10^7 J of energy she uses?

To solve this problem, we need to determine the amount of energy the cyclist uses during the 1-hour ride, and then calculate how much mass she loses based on the given energy-mass conversion rate.

Step 1: Calculate the total energy used by the cyclist during the 1-hour ride.
We know that power is the rate at which energy is expended, and it can be calculated using the formula:
Power = Force x Velocity

Given:
Average resistance (Force) = 22 N
Velocity = 5.8 m/s

Power = 22 N x 5.8 m/s
Power = 127.6 W (Watts)

To calculate the energy used by the cyclist, we need to find the total amount of energy (E) by multiplying the power (P) by the time (t):
Energy (E) = Power x time

Given:
Time (t) = 1 hour = 3600 seconds

Energy (E) = 127.6 W x 3600 s
Energy (E) = 459,360 Joules (J)

Step 2: Calculate the mass lost by the cyclist based on the energy-mass conversion rate.
Given:
1 kg is lost for each 2.9 x 10^7 J of energy used

We can set up a proportion to find the mass lost (m):
1 kg / 2.9 x 10^7 J = m / 459,360 J

Cross-multiplying and solving for m:
m = (1 kg x 459,360 J) / (2.9 x 10^7 J)
m ≈ 0.0158 kg

Therefore, the cyclist loses approximately 0.0158 kg of mass during the 1-hour ride.