This is a 2 part question, and I'm fine on part 1. However, for background info, here is part 1: A motorcycle racer traveling at 145km/h loses control in a corner of the track and slides across the concrete surface. The combined mass of the rider is 243kg. The steel of the motorcycle rubs against the concrete road surface. (a) What is the fricional force between the road and the motorcycle and rider (714N) (b) What would be the acceleration of the motorcycle and rider during the wipeout (-2.94m/s^2) and (c) Assuming there were no barriers to stop the motorcycle and rider, how long would it take the bike and the rider to slow to a stop? (13.7s).
This is the part I need help with:
The motorcycle and rider are sliding with the same acceleration as found above (-2.94m/s^2). If the motorcycle and rider have been sliding for 4.55s, what will be the force applied to the motorcycle and the rider when they strike the barrier and come to rest in another .530s? I have the answer (-1.23 x 104N), but have no idea how to arrive at the answer.
Any help would be greatly appreciated!
To calculate the force applied to the motorcycle and rider when they strike the barrier and come to rest, we can use Newton's second law of motion:
Force = mass × acceleration
Given:
Acceleration (a) = -2.94 m/s^2
Time (t1) = 4.55 s
Time (t2) = 0.530 s
First, let's calculate the final velocity of the motorcycle and rider when they strike the barrier. We can use the equation of motion:
Final velocity = Initial velocity + (acceleration × time)
Since the initial velocity is not given explicitly, we can assume it is zero since the object is coming to rest. Therefore, the final velocity can be calculated as:
Final velocity = 0 + (-2.94 m/s^2) × (4.55 s)
Next, let's calculate the change in velocity (Δv) from the time they start sliding till they strike the barrier:
Δv = acceleration × time
Δv = (-2.94 m/s^2) × (4.55 s)
Now, we can calculate the average force applied using Newton's second law:
Force = mass × acceleration
The mass to be considered here is 243 kg (combined mass of the motorcycle and rider). Therefore, the average force applied can be calculated as:
Force = 243 kg × (-2.94 m/s^2)
Finally, to find the force when they strike the barrier, we need to consider the change in momentum (Δp) and divide it by the time taken (t2):
Force = Δp / t2
Force = (mass × Δv) / t2
Now, let's plug in the values to calculate the force applied to the motorcycle and rider when they strike the barrier and come to rest:
Δv = (-2.94 m/s^2) × (4.55 s)
Force = (243 kg) × Δv / t2
Force = (243 kg) × [(-2.94 m/s^2) × (4.55 s)] / 0.530 s
By evaluating the above expression, we can find the force applied to the motorcycle and rider when they strike the barrier and come to rest.
To find the force applied to the motorcycle and rider when they strike the barrier, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = ma). In this case, the acceleration is the same as before (-2.94 m/s^2), and we need to determine the force.
First, let's calculate the velocity of the motorcycle and rider using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. We can assume the initial velocity is zero because they start from rest (after sliding for 4.55s).
Using the given time of 4.55s and the acceleration of -2.94 m/s^2, we can calculate the final velocity:
v = 0 + (-2.94 m/s^2) * 4.55s
v = -13.367 m/s (Since it's a deceleration, the velocity is negative)
Now that we have the final velocity, we can calculate the distance traveled using the equation s = ut + (1/2)at^2, where s is the distance, u is the initial velocity, a is the acceleration, and t is the time:
s = 0 * 4.55s + (1/2) * (-2.94 m/s^2) * (4.55s)^2
s = -30.8346 m (Again, the negative sign indicates the direction of deceleration)
So, after sliding for 4.55s, the motorcycle and rider have traveled a distance of -30.8346 m.
To find the force applied when they strike the barrier, we need to determine the change in momentum. Momentum (p) is given by the product of mass (m) and velocity (v), so the change in momentum (Δp) can be calculated as follows:
Δp = mvf - mvi
Δp = (mass of motorcycle and rider) * (-13.367 m/s) - (mass of motorcycle and rider) * (0 m/s)
Δp = (243 kg) * (-13.367 m/s)
Finally, to find the force (F) applied when they strike the barrier, we divide the change in momentum by the time it takes for them to stop moving (0.530s):
F = Δp / t
F = [(243 kg) * (-13.367 m/s)] / 0.530s
Calculating this expression gives us approximately -1.23 x 10^4 N (or -12,300 N), which is the force applied to the motorcycle and rider when they strike the barrier. The negative sign indicates that the force is opposite to the direction of motion (deceleration).