Concept explainers
Three objects are connected on a table as shown in Figure P5.14. The coefficient of kinetic friction between the block of mass m2 and the table is 0.350. The objects have masses of m1 = 4.00 kg, m2 = 1.00 kg, and m3 = 2.00 kg, and the pulleys are frictionless. (a) Draw a free-body diagram of each object. (b) Determine the acceleration of each object, including its direction. (c) Determine the tensions in the two cords. What If? (d) If the tabletop were smooth, would the tensions increase, decrease, or remain the same? Explain.
Figure P5.14
(a)
Draw free body diagram of the each object.
Answer to Problem 14P
The free body diagram of the mass of block
The free body diagram of the mass of block
The free body diagram of the mass of block
Explanation of Solution
The free body diagram is the graphical illustration used to visualize the movements and forces applied on a body.
Let
The free body diagram of the mass of block
The free body diagram of the mass of block
The free body diagram of the mass of block
Conclusion:
Therefore, the free body diagram of the mass of block
(b)
The magnitude and direction of acceleration of each object.
Answer to Problem 14P
The magnitude of acceleration of each object is
Explanation of Solution
Apply Newton’s second law for in the
Here,
From the Figure 1, write the expression for net force in the
Here,
Substitute,
From the Figure 2, write the expression for net force in the
Since,
Here,
From the Figure 2, write the expression for net force in the
From the Figure 3, write the expression for net force in the
Add equation (III), (IV), and (VI).
Write the expression for normal force for mass
Use,
Conclusion:
Substitute,
Therefore, the magnitude of acceleration of each object is
(c)
The tension in the two cords.
Answer to Problem 14P
Tension in the first code is
Explanation of Solution
Conclusion:
Substitute,
Substitute,
Therefore, tension in the first code is
(d)
Whether the tension increase, decrease, or remain the same if the tabletop were smooth.
Answer to Problem 14P
The tension in the left rope will decreases, and the tension in the right rope will increases.
Explanation of Solution
If the table top is smooth, the friction on the top will disappear. So the acceleration become larger.
From the equation (III),
Conclusion:
Therefore, the tension in the left rope will decreases, and the tension in the right rope will increases.
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Chapter 5 Solutions
Principles of Physics: A Calculus-Based Text
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