A bicyclist of mass 60 (including the bicycle) can coast down a 9.0 hill at a steady speed of because of air resistance.
Part A
How much force must be applied to climb the hill at the same speed and same air resistance?
To find out how much force must be applied to climb the hill at the same speed and air resistance, we need to understand the forces acting on the bicyclist when coasting down the hill.
When the bicyclist is coasting down the hill at a steady speed due to air resistance, the net force acting on the bicyclist is zero. This means that the force of gravity pulling the bicyclist down the hill is balanced by the force of air resistance pushing against them.
Now, when the bicyclist is climbing the hill at the same speed and same air resistance, we need to determine the additional force required to counteract the force of gravity pulling them downhill.
The force of gravity pulling the bicyclist downhill can be calculated using the formula:
Force of gravity = mass × acceleration due to gravity
Given that the mass of the bicyclist is 60 kg (including the bicycle), and the acceleration due to gravity is approximately 9.8 m/s^2, we can find the force of gravity acting on the bicyclist.
Force of gravity = 60 kg × 9.8 m/s^2 = 588 N
To climb the hill at the same speed and air resistance, an additional force of 588 N needs to be applied to counteract the force of gravity pulling the bicyclist downhill. This force can be applied by the bicyclist themselves by pedaling or by an external force pushing or pulling the bicyclist up the hill.
So, the answer to Part A is that the force to climb the hill at the same speed and same air resistance is 588 N.