7. (a) Figure 1 shows a cyclist going up a hill.
Figure 1
The angle
The total mass
Write an expression for the component of the total weight parallel to the slope.
(b) The useful power output of the cyclist is
The cyclist has a steady speed of
Assume that air resistance is negligible at this speed.
Calculate
(1)
Calculate
(5)
Step 1 :Given the power output (P) of the cyclist as 310 W, the total mass (m) as 65 kg, and the steady speed (V) as 1.63 m/s. We need to find the angle θ of the slope. We know that the component of the total weight parallel to the slope is given by
Step 2 :First, we need to find the force (F) acting on the cyclist parallel to the slope. We can do this by dividing the power (P) by the velocity (V):
Step 3 :Substitute the given values:
Step 4 :Now that we have the force (F) acting on the cyclist parallel to the slope, we can use the equation
Step 5 :Substitute the values and solve for θ:
Step 6 :