In Figure 5-66, a force F of magnitude 7 N is applied to a FedEx box of mass m 2

Question

In Figure 5-66, a force F of magnitude 7 N is applied to a FedEx box of mass m2 = 1.0 kg. The force is directed up a plane tilted by = 37°. The box is connected by a cord to a UPS box of mass 3.0 kg on the floor. The floor, plane, and pulley are frictionless, and the masses of the pulley and cord are negligible. What is the tension in the cord?

Question Part Points Submissions Used In Figure 5-66, a force F of magnitude 7 N is applied to a FedEx box of mass m2 = 1.0 kg. The force is directed up a plane tilted by i¸ = 37A degree . The box is connected by a cord to a UPS box of mass 3.0 kg on the floor. The floor, plane, and pulley are frictionless, and the masses of the pulley and cord are negligible. What is the tension in the cord?

Explanation / Answer

assume tension in the cord is T

Drawing the free body diagram for the FedEx box we have,

F-T-m2*g*sin37= m2 * a1 ( a1 is the acceleration of the box upwards along the incline).

Similarly free body diagram for UPS box would be

T= m1 * a2 ( m1= 3.kg and a2 is the acceleration of box along the horizontal)

Also since the cord is non-stretchable therefore a1=a2 and both have to move together only otherwise the cord will become slack and no tension then


(F-T- m2 * g * sin37)/m2= T/m1

(7-T-5.90)/1=T/3

(1.1-T)=T/3

3.3-3.3T=T

4.3T=3.3

T=0.7674N

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