A wood block (m=4.00kg) rests on top of a steel ramp, as shown in the figure abo

Question

A wood block (m=4.00kg) rests on top of a steel ramp, as shown in the figure above. (For wood on steel u sub s = 0.650 u sub k = 0.250). The ramp is initially horizontal, but it's slope, theta, is slowly increased until the block begins to slide. At this slope what is the speed of the block after it slides a distance of 2.00 m? A wood block (m=4.00kg) rests on top of a steel ramp, as shown in the figure above. (For wood on steel u sub s = 0.650 u sub k = 0.250). The ramp is initially horizontal, but it's slope, theta, is slowly increased until the block begins to slide. At this slope what is the speed of the block after it slides a distance of 2.00 m? A wood block (m=4.00kg) rests on top of a steel ramp, as shown in the figure above. (For wood on steel u sub s = 0.650 u sub k = 0.250). The ramp is initially horizontal, but it's slope, theta, is slowly increased until the block begins to slide. At this slope what is the speed of the block after it slides a distance of 2.00 m?

Explanation / Answer

the angle at which the block is ready to move is theta = atan(mu_s) = atan(0.65) = 33 degrees

intial speed is u = 0 m/s

final speed is v = ?

apply work energy theorem

Work done by net force = m*g*l*sin(33) - 0.5*m*v^2

[(m*g*sin(33))-(mu_k*m*g*cos(33))]*2 = m*g*l*sin(33) - 0.5*m*v^2

[(9.81*sin(33))-(0.25*9.81*cos(33))]*2 = 9.81*2*sin(33)-0.5*v^2

0.5*v^2 =10.68 -6.57

v = 2.86 m/s

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