- #1
Jennings
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Homework Statement
A car weighing 1940lb has lost its brakes and is unable to come to a stop. A police cruiser of 3900lb gets ahead of it so that the two cars are now bumper to bumper. The combined cars are now traveling at 60mph down a 15 degree grade slope. If the police cruiser can normally brake from 60mph to rest in 250ft if it is on level ground:A) How long will it take for the police cruiser to bring both cars to a stop?
B) How far will they have traveled during this time?
Ignore friction. [/B]
Homework Equations
[/B]F= ma
V^2 - Vo^2 = 2a∆x
The Attempt at a Solution
The first thing i did was convert everything into SI units for simplicity.
Speed of Cars
26.8 m/s
Mass of car
881kg
Mass of police cruiser
1770kg
Weight of car
8643N
Weight of police cruiser
17360N
Weight of Combined Cars
26000N
I then determined the breaking force Fb of the police cruiser's brakes by determining first the acceleration of caused by the brakes, and then finding the force using F=ma
[V^2 - Vo^2] / [2∆x] = a
ab= [0 - (26.8m/s)^2]/[2(76.3m)] = -4.71m/s^2
Fb=mab
F=(1770kg)(-4.71m/s^2) = -8337N
So the force applied by the brakes of the police is -8337N
The next thing i did was draw a free body diagram of the cars going down a 15 degree slope.
So if the cars are currently moving at a speed of 26.8m/s down the slope, this means they are not accelerating? right? I am confused about what to do next .
∑Fx = Wx - Fbx ??