Roger N. answered • 03/02/18

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4.9
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. BE in Civil Engineering . Senior Structural/Civil Engineer

A contestant in a winter games event pushes a 48.0 kg block of ice across a frozen lake with a rope over his shoulder at a 25 degree angle.

The coefficient of kinetic friction is 0.03.

A.) Calculate the minimum force F (in N) he must exert to get the block moving.

B.) What is its acceleration (in m/s^2) once it starts to move, if that force is maintained?

The coefficient of kinetic friction is 0.03.

A.) Calculate the minimum force F (in N) he must exert to get the block moving.

B.) What is its acceleration (in m/s^2) once it starts to move, if that force is maintained?

Solution:

A) First calculate weight of block W=mg = 48 kg x9.81 m/s

^{2}=470.9 NThe force of friction opposite to the direction of motion is:

f=µ

_{s}N where µ_{s}is coefficient of static friction = 0.1 N is the normal force of the ground pushing on the ice

In a free body diagram W=mg=N and,

N = 470.9 N , The friction force f=µ

_{s}N=0.1x470.9N=47.09 Nthe person must overcome the static friction force for the block of ice to start moving. Again in a free body diagram F = f = 47.09 N

the force he must pull at 25 degree is F/cos 25 = 47.09/cos25 =51.95 N or approximately 52 N

B) once the block start moving, the force must overcome the kinetic friction force f

_{k}. Using ∑F =ma , in the free body diagramF-f

_{k}=ma, f_{k}= Wµ_{k}= 470.9 N x 0.03 = 14.13 NThen: (47.09 N - 14.13 N) = (48 kg)(a), a= (32.96 N/48 kg) = 0.69 m/s

^{2}