A 64 kg bicyclist rides his 7.7 kg bicycle with a speed of 13.5 m/s.
How much work must be done by the brakes to bring the bike and rider to a stop?
How far does the bicycle travel if it takes 4.5 s to come to rest?
What is the magnitude of the braking force?
I know the work in the first question is -6.43366 kJ but I have no idea how to find the distance and force.
average velocity= 13.5m/s * 1/2
distance= avgvelocity*time
force*distance= initial KE
solve for force.
To find the answers to the second and third questions, you need to understand the concept of work, as well as the equations and principles related to it. Let's break it down step by step:
1. Work:
Work is defined as the amount of energy transferred to or from an object by means of a force acting on it. In this case, the force being applied is by the brakes to bring the bike and rider to a stop.
2. Work-Energy Principle:
According to the work-energy principle, the work done on an object is equal to the change in its kinetic energy. This principle can be mathematically expressed as:
Work = Change in Kinetic Energy
Now let's tackle each question individually:
1. How much work must be done by the brakes to bring the bike and rider to a stop?
To find the work done by the brakes, we need to calculate the change in kinetic energy of the bike and rider. The initial kinetic energy of the system (bike and rider) is given by:
Initial Kinetic Energy = 0.5 * Mass of Bike and Rider * (Velocity)^2
In this case, the mass of the bike and rider is 64 kg + 7.7 kg = 71.7 kg, and the velocity is 13.5 m/s.
The final kinetic energy is zero since the bike comes to a stop. Therefore, the change in kinetic energy is:
Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy
= 0 - Initial Kinetic Energy
Substituting the given values, the initial kinetic energy equals:
Initial Kinetic Energy = 0.5 * 71.7 kg * (13.5 m/s)^2
To calculate the work done by the brakes, we use the work-energy principle:
Work = Change in Kinetic Energy
Substitute the value of the change in kinetic energy to find the work done by the brakes.
2. How far does the bicycle travel if it takes 4.5 s to come to rest?
To calculate the distance traveled by the bicycle, we need to use the equation of motion relating distance, initial velocity, time, and acceleration:
Distance = Initial Velocity * Time + 0.5 * Acceleration * Time^2
Since the bicycle starts from an initial velocity of 13.5 m/s and comes to rest (final velocity = 0 m/s), the equation becomes:
Distance = 13.5 m/s * 4.5 s + 0.5 * Acceleration * (4.5 s)^2
Substitute the given values of initial velocity and time to find the distance traveled.
3. What is the magnitude of the braking force?
The magnitude of the braking force can be found using Newton's second law of motion, which states that force is equal to mass multiplied by acceleration:
Force = Mass * Acceleration
To find the acceleration, we can use the equation of motion relating distance, initial velocity, final velocity, and acceleration:
Final Velocity^2 = Initial Velocity^2 + 2 * Acceleration * Distance
Since the final velocity is zero, the equation becomes:
0 = (13.5 m/s)^2 + 2 * Acceleration * Distance
From this equation, we can find the value of acceleration. Once the acceleration is known, substitute it along with the mass of the bike and rider to calculate the magnitude of the braking force using Newton's second law.
Please note that the calculations may involve rounding to an appropriate number of decimal places based on the level of precision required.