Lou bets an innocent stranger that he can place a 8 kg block against the side of

Question

Lou bets an innocent stranger that he can place a 8 kg block against the side of a cart, as in the figure below, and that the block will not fall to the ground, even though Lou will use no hooks, ropes, fasteners, magnets, glue, or adhesives of any kind. When the stranger accepts the bet, Lou begins to push the cart in the direction shown. The coefficient of static friction between the block and the cart is 0.4.

1)

(a) Find the minimum acceleration for which Lou will win the bet.
m/s2

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2)

(b) What is the magnitude of the frictional force in this case?
N

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3)

(c) Find the force of friction on the block if a is twice the minimum needed for the block not to fall.

N

(d) Show that, for a block of any mass, the block will not fall if the acceleration is a g/ s, where s is the coefficient of static friction. (Do this on paper. Your instructor may ask you to hand this in.)

Explanation / Answer

here,

mass of the block , m = 8 kg

coefficient of kinetic friction , uk = 0.4

1)

let the accelration be a

for the block to not to fall

frictional force = m*g

uk*m*a = m*g

0.4 * a = 9.8

a = 24.5 m/s^2

the accelration must be 24.5 m/s^2

2)

magnitude f frictional force , ff = uk *m*a

ff = 0.4 *8 * 24.5

ff = 78.4 N

the magnitude of the frictional force is 78.4 N

3)

if a' = 2*a = 49 m/s^2

friction force , ff   = uk *m*a

ff = 0.4 *8 * 49

ff = 156.8 N

the magnitude of the frictional force is 156.8 N

4)

for the block to not to fall

frictional force >= m*g

uk*m*a >= m*g

a >= g/uk

therefore the block will not fall if a >=g/uk , and does not depend on the mass

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