A young girl (m= 30 kg) rides a skateboard (m= 3.2 kg) at a speed of 4.2 m/s.
(a)
How much work does
the girl have to do to bring herself to a stop?
(b)
How far does she travel if it takes 6.0 s to stop?
(c)
What
is the magnitude of the stopping force?
So I know W=Fd, but I am having trouble figuring out how to factor in her stopping. Does her stopping make a final velocity of 0? Help! So confused.
To solve this problem, we need to apply the laws of motion and use the concept of work and energy.
(a) To find the work done by the girl to bring herself to a stop, we can use the work-energy principle. The principle states that the work done on an object is equal to the change in its kinetic energy. The initial kinetic energy of the girl-skateboard system is given by:
Initial kinetic energy = 0.5 * mass * velocity^2
Since the speed is given as 4.2 m/s, the initial kinetic energy is:
Initial kinetic energy = 0.5 * (30 kg + 3.2 kg) * (4.2 m/s)^2
To bring the girl-skateboard system to a stop, the final kinetic energy will be zero. Therefore, the work done by the girl to stop is equal to the initial kinetic energy:
Work = Initial kinetic energy = 0.5 * (33.2 kg) * (4.2 m/s)^2
(b) To find the distance traveled by the girl when it takes 6.0 s to stop, we use the equation of motion:
Final velocity = Initial velocity + (acceleration * time)
In this case, the acceleration is negative as it is the deceleration due to stopping. The initial velocity is 4.2 m/s, and the final velocity is 0 m/s (stopping). Rearranging the equation, we get:
Acceleration = (Final velocity - Initial velocity) / time
To find the distance traveled, we use the equation:
Distance = (Initial velocity * time) + (0.5 * acceleration * time^2)
Substitute the values to find the distance traveled.
(c) The magnitude of the stopping force can be found using Newton's second law of motion:
Force = mass * acceleration
In this case, the mass is the total mass of the girl and the skateboard (33.2 kg) and the acceleration is the negative acceleration used to stop the girl-skateboard system. Use the value of acceleration obtained in part (b) to calculate the magnitude of the stopping force.
Remember to convert units if necessary and plug in the numbers to find the final answers.