Concept explainers
Two boxes with masses m1 = 4.00 kg and m2 = 10.0 kg are attached by a massless cord passing over a frictionless pulley as shown in Figure P5.79. The incline is frictionless, and θ = 30.0°.
- a. Draw a free-body diagram for each of the boxes.
- b. What is the magnitude of the acceleration of the boxes?
- c. What is the tension in the cord connecting the boxes?
- d. What is the speed of each of the boxes 3.00 s after the system is released from rest?
FIGURE P5.79
(a)
Draw the free body diagram for each of the boxes.
Answer to Problem 79PQ
The free body diagram for each of the boxes is given below.
Explanation of Solution
The free body diagram each of the boxes is given below.
Conclusion:
(b)
Find the acceleration of the boxes.
Answer to Problem 79PQ
The acceleration of the boxes is
Explanation of Solution
Applying Newton’s laws,
Here,
Here,
Substitute equation II in equation I.
Conclusion:
Substitute
Therefore, the acceleration of the boxes is
(c)
Find the tension in the cord connecting the boxes.
Answer to Problem 79PQ
The tension in the cord connecting the boxes is
Explanation of Solution
Use the equation II to find the tension in the rope connecting the two sleds.
Conclusion:
Substitute
Therefore, the tension in the rope connecting the two sleds is
(d)
Find the speed of the boxes
Answer to Problem 79PQ
The speed of the boxes
Explanation of Solution
As the boxes are at rest initially, write the equation of final speed.
Here,
Conclusion:
Substitute
Therefore, the speed of the boxes
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