Solving the Impulse-Momentum Equation for a Coasting Car

  • Thread starter Thread starter madahmad1
  • Start date Start date
  • Tags Tags
    Car
AI Thread Summary
A coasting car with a mass of 1000 kg slows from 100 km/h to 50 km/h on a 10-degree slope over 8 seconds. The impulse-momentum equation is applied to determine the average braking force exerted by the road, which is calculated to be approximately 3400 N. The net force is derived from the equation F = mdv/dt, considering the car's acceleration and the effects of gravity on the slope. The discussion also raises a question about the terminology of the "impulse-momentum equation" in relation to Newton's second law. Overall, the calculations and concepts align to solve for the braking force effectively.
madahmad1
Messages
42
Reaction score
0

Homework Statement



A coasting car with a mass of 1000 kg has a speed of 100 km/h down a 10
degree slope when the brakes are applied. if the car is slowed to a speed of 50
km/ h in 8s, compute using the impulse-momentum equation the average of the total braking force exerted by the road on all the tires during the period. Treat the car as a particle and neglect air resistance.


Homework Equations





The Attempt at a Solution


The impulse-momentum equation states that the sum of Forces F = mdv/dt
so we turn this equation into an integral and solve, I know that the answer is 3400 N but do not know how to get it. any help?
 
Physics news on Phys.org
For this, I'm going to take up the ramp to be the positive direction and down the ramp to be the negative direction.

Let F be the net force (this should end up being positive, since the initial velocity is negative, based on the definition above, and the car is slowing down).
Let f be the frictional force (should be positive, for the same reasons).

By drawing the FBD, you should see that:

F = f - mg \sin 10 ^\circ
OR:
f = F + mg \sin 10 ^\circ

Also, we know the average acceleration of the car, so we know F:

F = m \frac{dv}{dt} = ma = m \frac{ (- \frac{50}{3.6})-(-\frac{100}{3.6}) }{ 8 } = m \frac{50}{8*3.6}

The rest is pretty obvious (I got 3439 N, which I figure is close enough).

I'm not sure why you would want to integrate F = mdv/dt, since you're looking for a force.

Just out of curiosity, which form of Newton's 2nd law were you taught is called the "impulse-momentum equation"? It's the first time I've heard the term used.
 

Similar threads

Replies
3
Views
4K
Replies
15
Views
3K
Replies
4
Views
3K
Replies
9
Views
4K
Replies
1
Views
2K
Replies
29
Views
3K
Back
Top