A Crate is Dragged A 67 kg crate is dragged across a floor by pullingon a rope a

Question

A Crate is Dragged A 67 kg crate is dragged across a floor by pullingon a rope attached to the crate and inclined 15° above thehorizontal. (a) If the coefficient of static friction is0.48, what minimum force magnitude isrequired from the rope to start the crate moving?
1 N
(b) If µkin = 0.33,what is the magnitude of the initial acceleration of the crate?
2 m/s2
(a) If the coefficient of static friction is0.48, what minimum force magnitude isrequired from the rope to start the crate moving?
1 N
(b) If µkin = 0.33,what is the magnitude of the initial acceleration of the crate?
2 m/s2

Explanation / Answer

mass m = 67 kg angle = 15 degrees (a). coefficient of static friction = 0.48 Minimum force magnitude is required from the rope to start thecrate moving = static frictional force T cos = [ mg - T sin ] 0.9659 T = 315.168 -0.1242 T            T = 289.1 N

(b) µkin = 0.33 the magnitude of the initial acceleration of thecrate a = ( T cos - f ' ) / m where f ' = kinetic frictional force = 0.33 [ mg -T sin ]               = 0.33 [ 656.6 - 74.82 ]               = 191.9874 N So, accleration a = [ 279.24 - 191.9874 ] / 67                           = 1.3 m / s ^ 2 the magnitude of the initial acceleration of thecrate a = ( T cos - f ' ) / m where f ' = kinetic frictional force = 0.33 [ mg -T sin ]               = 0.33 [ 656.6 - 74.82 ]               = 191.9874 N So, accleration a = [ 279.24 - 191.9874 ] / 67                           = 1.3 m / s ^ 2

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