A cyclist of total mass 85 kg maintains a constant speed up an inclined plane. the plane is inclined at 20 degrees to the horizontal. with frictional force of 120 N. the cyclist covers a distance of 50 m along the inclined plane in 20 s.
1. Calculate the work done by the cyclist's applied force
2. Calculate the average power output of the cyclist.
1. Fx = Fg sin 20
85 x 9.8 x sin 20
284.9
284.9 + 120 = 404. 9 (not in direction of the force)
404.9 x 50 = 20245 but answer behind book [without calculations] is 20145 please help
To calculate the work done by the cyclist's applied force, we first need to determine the component of the cyclist's weight that acts along the direction of motion. The formula you used, Fx = Fg sin 20, is correct.
Fg is the force due to gravity acting on the cyclist, which is equal to the mass (85 kg) multiplied by the acceleration due to gravity (9.8 m/s^2).
Fx = 85 kg x 9.8 m/s^2 x sin 20°
Fx = 284.9 N
Next, we need to take into account the frictional force of 120 N. Since the frictional force is acting in the opposite direction of motion, we subtract it from Fx to get the net force in the direction of motion:
Net force = Fx - Frictional force
Net force = 284.9 N - 120 N
Net force = 164.9 N
To calculate the work done, we multiply the net force by the distance traveled along the inclined plane:
Work done = Net force x Distance
Work done = 164.9 N x 50 m
Work done = 8245 J
Therefore, the work done by the cyclist's applied force is 8245 Joules.
As for calculating the average power output of the cyclist, we can use the formula:
Power = Work done / Time
Given that the distance covered is 50 m and the time taken is 20 s:
Power = 8245 J / 20 s
Power ≈ 412.25 W
Therefore, the average power output of the cyclist is approximately 412.25 Watts.