A 33.3 kg cyclist is riding a 10.7 kg bicycle at a velocity of 7.0 m/s. If the cyclist applies a brake that applies a force of 42.7 N, what is the time required for the cyclist to come to a stop?
To find the time required for the cyclist to come to a stop, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
The net force acting on the cyclist-bicycle system can be calculated by subtracting the force applied by the brake from the force generated by the combination of the cyclist and the bicycle.
The force generated by the combination of the cyclist and the bicycle can be calculated using the equation:
Force = Mass × Acceleration
The acceleration of the cyclist-bicycle system can be calculated using the equation:
Acceleration = Change in velocity / Time
Since the cyclist comes to a stop, the change in velocity is equal to the initial velocity of the cyclist-bicycle system.
Let's calculate step by step:
1. Calculate the force generated by the combination of the cyclist and the bicycle:
Force = (mass of the cyclist + mass of the bicycle) × acceleration
= (33.3 kg + 10.7 kg) × acceleration
= 44 kg × acceleration
2. Calculate the acceleration of the cyclist-bicycle system:
Acceleration = Change in velocity / Time
= Initial velocity / Time
= 7.0 m/s / Time
= 7.0 / Time m/s²
3. Set up an equation using Newton's second law of motion:
Force - Force_applied_by_brake = mass × acceleration
44 kg × acceleration - 42.7 N = (33.3 kg + 10.7 kg) × acceleration
4. Solve the equation for acceleration:
44 kg × acceleration - 42.7 N = 44 kg × acceleration
-42.7 N = 0 kg × acceleration
Since the acceleration cancels out, we are left with:
-42.7 N = 0
Since there is no acceleration, the forces are balanced when the cyclist comes to a stop.
Therefore, the time required for the cyclist to come to a stop is instantaneous. The cyclist stops immediately when the brake is applied.
force*:time=changemomentum
42.7*time=(33.3+10.7)(7.0)
solve for time