?A 7.35-kg box is pulled up a ramp that is inclined at an angle of 37.0° with re

Question

?A 7.35-kg box is pulled up a ramp that is inclined at an angle of 37.0° with respect to the horizontal, as shown below. The coefficient of kinetic friction between the box and the ramp is 0.155, and the rope pulling the box is parallel to the ramp. If the box accelerates up the ramp at a rate of 2.09 m/s2, what must the tension FT in the rope be? Use g = 9.81 m/s2 for the acceleration due to gravity.

A 7.35-kg box is pulled up a ramp that is inclined at an angle of 37.0° with respect to the horizontal, as shown below. The coefficient of kinetic friction between the box and the ramp is 0.155, and the rope pulling the box is parallel to the ramp. If the box accelerates up the ramp at a rate of 2.09 m/s2, what must the tension Fr in the rope be? Use g 9.81 m/s2 for the acceleration due to gravity. ent of kinetic friction betw Number a-2.09 m /s2 m=7.35 kg = 0.155 = 37.0

Explanation / Answer

Resolve vertically
N-mgcos37=0
N=mgcos37

Resolve horizontally
T-mgsin37-Ff=ma
Ff=uN
Ff=umgcos37
T-mgsin37-umgcos37=ma
T=ma+mgsin37+umgcos37
u=0.155, a=2.09m/s2, m=7.35, g=9.81 lets sub in these values
T=(7.35)(2.09)+(7.35)(9.81sin37)+(0.155)(7.35)(9.81cos37)
T=67.68N
Answer: The tension in the rope is 67.68N

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