A flat cart of mass M can move on a horizontal surfacewithout any friction. A bl

Question

A flat cart of mass M can move on a horizontal surfacewithout any friction. A

block of mass m sits on the surface of the cart and isattached to a massless string as shown. The coefficient ofstatic friction between the block and cart is s, andthe coefficient of kinetic friction between the block and thecart is k. Explain how you would goabout determining the value of the tension in the string thatwould cause the cart to have maximumacceleration.

Note: You are not required to solve this problem. Explain how you would go about solving it. Yourexplanation should be detailed enough to enable anotherstudent to solve the problem using your explanation.

Explanation / Answer

The maximum force the small block can exert on the large blockis the static friction force, which is given by .        s mg   . So the cart would have max acceleration when the max staticfriction force is used. Also, the acc of the small block would bethe same as that of the cart, since it is on the cart. . You then would analyze the forces acting on the small blockusing Newton's second law: .        total forces = m a .        Tension - static friction force =   m a .          T -    s m g   =   m a . and you could calculate the acceleration of the small blockunder these circumstances. And of course... that would also be theacceleration of the cart! . Done.

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