A contestant in a winter games event pushes a 44.0 kg block of ice across a froz

Question

A contestant in a winter games event pushes a 44.0 kg block of ice across a frozen lake with a rope over his shoulder as shown in Figure 4.29(b). The coefficient of static friction is 0.1 and the coefficient of kinetic friction is 0.03.

A contestant in a winter games event pushes a 44.0 kg block of ice across a frozen lake with a rope over his shoulder as shown in Figure 4.29(b). The coefficient of static friction is 0.1 and the coefficient of kinetic friction is 0.03. (a) Calculate the minimum force F he must exert to get the block moving. 1 N What is its acceleration once it starts to move, if that force is maintained? 2 m/s2

Explanation / Answer

For your question :-

for digram (b)

the applied for is at angle of 25 degrees

hence it will be divided into two parts one is horizontal part and another one is vertical part

horizontal part is equal to

F cos(25) = 0.906F

vertical part is equal to

F sin(25) = 0.422F

now force of friction which opposes the forward motion of block is equal to = Ff = coefficient of static friction * normal force

F of friction = 0.1 ( 44*9.81 - 0.422 F ) = 43.164 - 0.0422F

when the horizontal force exceeds this value then the block start moving .

0.906F = 43.164 -0.0422F

=> 0.906F - 0.0422F = 43.164

=> 0.8638 F = 43.164

=> F = 49.97 N

2-> when the block start moving then the force of friction is equal to

0.03 ( 44* 9.81 - 0.422 F ) = 12.95 - 0.63 = 12.32 N

apply newtons secound law of motion F = ma

49.97 - 12.32 = 44 *a

=> a= 37.65/44 = 0.855 m/s2

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