Fred Flintstone is getting ready to go to work in the morning. Of course, if you

Question

Fred Flintstone is getting ready to go to work in the morning. Of course, if you were properly indoctrinated, you would know he gets his "car" going by putting his feet through the bottom of the car and running to push the car forward. The car's mass is 500kg, and it's coefficient of rolling friction is 0.04. Fred's mass is 100kg. (Hint: In this problem the friction force pushes forward, since his feet are peddling backwards. So, the forward push is limited by the friction force that can be produced by Fred's feet and the ground. Remember that the mass Fred needs o accelerate is equal to Fred's mass + the car's mass.)
a. Initially, Fred's feet slide on the ground before the car gets going with a sliding coefficient of friction of 0.40. What is the maximum acceleration of Fred and the car?
b. Once he gets going, he runs normally and has a static coefficient of friction of 0.95. What is the maximum acceleration of Fred and the car?
Please show each step and explain clearly and i will give A+.
Thanks!

Explanation / Answer

(a)rolling friction on the car,Fr=.04*500*9.8=196N which will be directed opposite to the motion.

frictional force on fred,Ff = 0.4 x mass of fred x g = 0.4 x 100 x 9.81 = 392 N

so the total force acting,Fnet = Ff-fr=196N

so the net acceleration=Fnet/total mass=196/600=0.33m/s^2

 

(b) force due to static friction which will act on fred, Fs =  0.95x 100 x 9.8 = 931 N

force due to rolling friction, Fr = 0.04 x 500 x 9.8 = 196N

total force acting=Fs-Fr= 735N

so, net acceleration,=Fnet/total mass=735/600=1.23m/s^2(if we take g=10m/s2 we get the answer as 1.25m/s^2)

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