A 70kg bicyclist, initially at rest at the top of a hill, coasts down the hill. During her ride she experiences a 40N drag. The distance and height of the hill are shown. What’s the initial J
To find the initial J, we need to find the total work done on the bicyclist. Work is calculated using the equation:
Work = force * distance
In this case, the drag force of 40N is acting against the motion of the bicyclist. Therefore, the work done by the drag force is negative.
The work done by the drag force is given by:
Work_drag = - drag force * distance
To find the total work done on the bicyclist, we need to consider both the work done by the drag force and the work done by the weight of the bicyclist.
The work done by the weight of the bicyclist is equal to the change in potential energy, which is calculated as:
Work_weight = mass * gravity * height
where mass is the mass of the bicyclist (70kg), gravity is the acceleration due to gravity (9.8m/s^2), and height is the height of the hill.
Since the bicyclist is at rest at the top of the hill, the initial kinetic energy is zero.
The initial J, which is the initial mechanical energy, is equal to the sum of the initial potential energy and the initial kinetic energy:
Initial J = Initial potential energy + Initial kinetic energy
= Work_weight + 0 (since initial kinetic energy is zero)
= Work_weight
Therefore, the initial J is equal to the work done by the weight of the bicyclist:
Initial J = Work_weight
= mass * gravity * height
Substituting the given values:
Initial J = 70kg * 9.8m/s^2 * height
Thus, the initial J is given by 70kg * 9.8m/s^2 * height.