a 100 kg bicycle is riding on the sidewalk at 15m/s when the rider is 20m from the intersection a red light causes her to apply 50N force to stop the bicycle
To find the distance it takes for the bicycle to stop, we can use the concept of work and energy. The work done by the rider's force will be equal to the kinetic energy of the bicycle.
1. Calculate the initial kinetic energy of the bicycle:
The kinetic energy (KE) of an object is given by the formula: KE = (1/2)mv^2
Here, m = mass of the bicycle = 100 kg
And v = velocity of the bicycle = 15 m/s
Plugging in the values:
KE = 0.5 * 100 kg * (15 m/s)^2
KE = 0.5 * 100 kg * 225 m^2/s^2
KE = 11250 J
2. Calculate the work done by the rider's force:
Work (W) is given by the formula: W = force * distance
The rider applies a force of 50 N to stop the bicycle, and we need to find the distance it takes for the bicycle to stop.
Plugging in the values:
W = 50 N * distance
3. Equate the work done to the kinetic energy:
According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy. Therefore, we have:
W = KE
Plugging in the values:
50 N * distance = 11250 J
4. Solve for the distance:
Divide both sides of the equation by 50 N:
distance = 11250 J / 50 N
distance = 225 m
So, it takes a distance of 225 meters for the bicycle to come to a stop when the rider applies a force of 50 N.