Impulse for a car when it drives in a circle

[iamhe]

Homework Statement

A 1400kg car is driving at a constant velocity, 5.3 m/s. It turns 90 degrees in 4.6 seconds. And then it slams into a tree and it takes 350 ms to stop the car.
What is the impulse on the car (a) due to the turn? (b)Due to the collision with the tree?
What is the magnitude of the average force that acts on the car (c)during the turn? (d)During the collision with the tree?
What is the angle between the average force in (c) and the positive x direction?

Homework Equations

Impulse = j = p2-p1 = mv2-mv1
F = ma

The Attempt at a Solution

a) 0. Since the velocity does not change, and the mass is constant, there is no change between p1 and p2.
b) j = (1400)(5.3) - (1400)(0) = 7420
c) F = 0/(4.6) = 0
d) F = (7420)/(0.350) = 21200
e) I have absolutely no clue on how to even start this one.


Thanks in advance for any help!

 

[SHISHKABOB]

Well for the parts where the car is making the turn, there's a force that you might be forgetting about. Basically, during the turn, the car is in Uniform Circular Motion for a quarter of a circle.

 

[iamhe]

If I am not given the radius of the turn, how can I still use the uniform circular motion formula?

 

[SHISHKABOB]

You're given the time it took to make a quarter of a circle and you're given the tangential speed during the turn. There's a relationship between those that will give you the radius.

 

[asteriatic]

I would like to point out a few things about this scenario. First, it is important to note that the car is not driving in a perfect circle, as it turns 90 degrees and then collides with a tree. This means that the impulse and force values calculated may not accurately represent the car's motion in a circular path.

To answer the questions:

a) The impulse on the car due to the turn can be calculated using the formula j = p2-p1 = mv2-mv1. Since the car's velocity does not change in the turn, the impulse will be 0.

b) The impulse on the car due to the collision with the tree can be calculated using the same formula, j = p2-p1 = mv2-mv1. However, in this case, the car's final velocity is 0, so the impulse will be equal to the car's initial momentum, which is mv1 = (1400)(5.3) = 7420 kg*m/s.

c) The magnitude of the average force acting on the car during the turn can be calculated using the formula F = ma, where m is the mass of the car and a is the centripetal acceleration. The centripetal acceleration can be calculated using the formula a = v^2/r, where v is the car's velocity and r is the radius of the turn. However, since the turn is not a perfect circle, the radius is not given and the acceleration cannot be accurately calculated. Therefore, it is not possible to calculate the magnitude of the average force during the turn.

d) The magnitude of the average force acting on the car during the collision with the tree can be calculated using the formula F = ma, where m is the mass of the car and a is the deceleration of the car. The deceleration can be calculated by dividing the change in velocity (5.3 m/s) by the time it takes to stop (0.350 s). Therefore, the average force during the collision is F = (1400)(5.3)/0.350 = 21200 N.

e) The angle between the average force and the positive x direction cannot be accurately calculated without knowing the direction of the force and the orientation of the car at the time of the collision. It is also important to note that the force acting on the car during the collision may not be in the same direction as the force that