Physics Math

Question

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 static friction is 0.1 and 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?

Answer 1

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?

 

Solution:

 

A) First calculate weight of block W=mg = 48 kg x9.81 m/s²=470.9 N

 

The force of friction opposite to the direction of motion is:

 

f=µ_sN 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_sN=0.1x470.9N=47.09 N

 

the 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 diagram

 

F-f_k=ma, f_k= Wµ_k = 470.9 N x 0.03 = 14.13 N

 

Then:  (47.09 N - 14.13 N) = (48 kg)(a), a= (32.96 N/48 kg) = 0.69 m/s²