What am I solving for in this physics problem? And how do I get the answer?
Ke Min is driving at a speed of 23 m/s on a rainy night when he notices a tree branch lying across the road 60.0 m ahead. He slams on the brakes to try to stop in time. If the coefficient of kinetic friction between the car's locked tires and the wet road is 0.41, will the car stop before hitting the branch? The car has a mass of 2400 kg.
2 Answers
From Newton second Law :
-0.4*m*g=ma
-0.4*g=a if g = 10m/s^2 the a=-4 m/s^2
using :
v=vo+at assume v=0 if the car stop
0 = 23-4*t then t= 5.75 s
using :
s=vo*t+0.5*a*t^2 = 132.25-0.5*4*5.75*5.75=132.25-66.125 = 66.125 m..
So, the car does not stop…the car hit the branch..
The question is asking whether he will stop within the 60 metres before the tree branch. This is a kinematic equation.
First, we need to figure out the force due braking, and hence the decelleration.
We know that for friction, F = mu * mg. In this case, mu is 0.41, so F = 0.41 * 2400 * 9.81 = 9653.04
F = m a, 9653.04 = 2400 * a, a = 9563.04 / 2400 = 4.0221 m/s ( or -4.0221 m/s technically, as he is decellerating).
You should be able to figure the rest out with kinematics from here on.
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