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Car question

  1. May 8, 2008 #1
    1. The problem statement, all variables and given/known data

    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.

    2. Relevant equations

    3. 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?
  2. jcsd
  3. May 12, 2008 #2
    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:

    [tex]F = f - mg \sin 10 ^\circ[/tex]
    [tex]f = F + mg \sin 10 ^\circ[/tex]

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

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

    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.
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