Sam is using a rope to pull a box weighing 300 N across a floor with constant velocity. The rope makes an angle of 30o above the horizontal. If the tension in the rope is 100 N, what is the normal force that the floor exerts on the box?

A. 133 N
B. 250 N
C. 300 N
D. 400 N

Question

Sam is using a rope to pull a box weighing 300 N across a floor with constant velocity. The rope makes an angle of 30o above the horizontal. If the tension in the rope is 100 N, what is the normal force that the floor exerts on the box?


 A. 133 N 
 B. 250 N 
 C. 300 N 
 D. 400 N

anonymous · Answer

This is a vector addition problem Weight=300N is directed downward, -y direction, and the floor responds in the upward direction.

Sam's pulling is a vector that has a positive y-direction value of 100 sin(30)=50N,

This offsets the weight so that W' = 300N-50N= 250N

The x-component of Sam's pulling is 100 cos(30) = 87 N, used to offset friction.