Shopping cart full of groceries is rolling downhill, towards the street, you spr

Question

Shopping cart full of groceries is rolling downhill, towards the street, you spring towards it, attempting to stop it before it reaches the road. You catch hold of the cart a mere 10.0 m away from the road and stop it just in time at the edge of the street. When reviewing that just happened you learn that the street was angled at 30.0 degree and the cart had a mass of 80.0 kg with groceries included. You know you were almost at the limit of had a mass of 80.0 kg with groceries included. You know you were almost at the limit of your speed so the cart must have been going at 9.0^m/_s when you caught it. Find the Energy of the Cart at the time you grab hold of it. Choose the street level as you reference point for height. Find the total Work you do on the Cart plus the work of friction on the Cart. If the effective of kinetic friction is mu_k = 0.1, find the force with which you pulled back the cart. (Assume the force is in the direction opposite to the motion of the cart).

Explanation / Answer

(a)
Energy of the cart when you caught hold of it, = Kinetic Energy + Potential Energy
Energy of the cart, = 1/2*mv^2 + m*g*h
Energy of the cart, = 1/2*80.0*9.0^2 + 80.0*9.8*10*sin(30)
Energy of the cart, =  7160 J

(b)
As Final K.E = 0
Total Work done by you + Friction = 7160 J

(c)
Work done = Force with which you pull * distance + Friction force * distance
7160 = F*10 + uk*m*g*cos(30)*10
7160 = F*10 + 0.1*80*9.8*cos(30)*10
F = 648 N
Force with which you pulled back the cart, F = 648 N

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