Concept explainers
(a)
The mass M in terms of m, g , and
(a)
Answer to Problem 88AP
The mass M in terms of m, g , and
Explanation of Solution
The system is in equilibrium, so force on either sides of the pulley must be the same.
Write the expression for the equilibrium.
Here,
Conclusion:
Simplify the above equation.
Therefore, the mass M in terms of m, g, and
(b)
The tension
(b)
Answer to Problem 88AP
The tension
Explanation of Solution
Below figure shows the forces and tension acting on the string.
From the figure,
From the figure,
Conclusion:
Therefore, the tension
(c)
The acceleration of each object
(c)
Answer to Problem 88AP
The acceleration of each object is
Explanation of Solution
Below figure shows the forces and tension acting on the string.
Use Newton’s second law to write the expression for tension
Use Newton’s second law to write the expression for tension
Substitute
Use Newton’s second law to write the expression for tension
Conclusion:
Substitute equation (I) and (II) in (III) and simplify.
All the objects are connected to a single string and hence they have same acceleration.
Therefore, the acceleration of each object is
(d)
The tension
(d)
Answer to Problem 88AP
The tension
Explanation of Solution
Rewrite (I).
Rewrite (II).
Conclusion:
Substitute
Substitute
Therefore, the tension
(e)
The maximum value of
(e)
Answer to Problem 88AP
The maximum value of
Explanation of Solution
Below figure shows the forces acting on the system (including frictional force).
From the figure
Write the expression for friction force acting on
Here,
Write the expression for friction force acting on
Write the expression for tension
The system is in equilibrium,
Substitute 0 for
Similarly, Write the expression for tension
Substitute 0 for
Write the expression for
Substitute 0 for
Substitute
Conclusion:
Equate (V) and (VII).
Therefore, the maximum value of
(f)
The minimum value of
(f)
Answer to Problem 88AP
The minimum value of
Explanation of Solution
For minimum value of
Below figure shows the forces acting on the system (including frictional force).
Therefore,
Conclusion:
Equate both the above expression for
Therefore, the minimum value of
(g)
Comparison the values of
(g)
Answer to Problem 88AP
Comparison the values of
Explanation of Solution
Compare (IX) and (VIII).
Conclusion:
Therefore, the Comparison of the values of
Want to see more full solutions like this?
Chapter 5 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
- Two objects, m1 = 3.00 kg and m2 = 8.50 kg, are attached by a massless cord passing over a frictionless pulley as shown in Figure P5.51. Assume the horizontal surface is frictionless. a. Draw a free-body diagram for each of the two objects. b. What is the tension in the cord? c. What is the magnitude of the acceleration of the two objects? FIGURE P5.51 Problems 51 and 65.arrow_forwardA heavy chandelier with mass 125 kg is hung by chains in equilibrium from the ceiling of a concert hall as shown in Figure P5.77, with 1 = 37.0 and 2 = 64.0. Assuming the chains are massless, what are the tensions FT1, FT2, and FT3 in the three chains? FIGURE P5.77arrow_forwardTwo blocks connected by a rope of negligible mass are being dragged by a horizontal force (Fig. P5.13). Suppose F = 68.0 N, m1 = 12.0 kg, m2 = 18.0 kg, and the coefficient of kinetic friction between each block and the surface is 0.100. (a) Draw a free-body diagram for each block. Determine (b) the acceleration of the system and (c) the tension T in the rope. Figure P5.13arrow_forward
- Initially, the system of objects shown in Figure P5.49 is held motionless. The pulley and all surfaces and wheels are frictionless. Let the force F be zero and assume that m1 can move only vertically. At the instant after the system of objects is released, Find (a) the tension T in the string, (b) the acceleration of m2, (c) the acceleration of M, and (d) the acceleration of m1. (Note: The pulley accelerates along with the cart.) Figure P5.49 Problems 49 and 53arrow_forwardAn object of mass m1 = 5.00 kg placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging object of mass m2 = 9.00 kg as shown in Figure P5.22. (a) Draw free-body diagrams of both objects. Find (b) the magnitude of the acceleration of the objects and (c) the tension in the string. Figure P5.22 Problems 22 and 29.arrow_forwardConsider the three connected objects shown in Figure P5.88. Assume first that the inclined plane is friction-less and that the system is in equilibrium. In terms of m, g, and , find (a) the mass M and (b) the tensions T, and T2. Now assume that the value of Af is double the value found in part (a). Find (c) the acceleration of each object and (d) the tensions T1 and T2. Next, assume that the coefficient of static friction between m and 2m and the inclined plane is m, and that the system is in equilibrium. Find (e) the maximum value of M and (0 the minimum value of M. (g) Compare the values of T2 when M has its minimum and maximum values.arrow_forward
- 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 P5.14arrow_forwardTwo blocks are connected by a rope that passes over a massless and frictionless pulley as shown in Figure P5.41. Given that m0 = 15.93 kg and m2 = 10.45 kg, determine the magnitudes of the tension in the rope and the blocks acceleration. FIGURE P5.41arrow_forwardAn object of mass m1 = 5.00 kg placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging object of mass m2 = 9.00 kg as shown in Figure P4.28. (a) Draw free-body diagrams of both objects. Find (b) the magnitude of the acceleration of the objects and (c) the tension in the string. Figure P4.28arrow_forward
- Two blocks, each of mass m, are hung from the ceiling of an elevator as in Figure P4.33. The elevator has an upward acceleration a. The strings have negligible mass. (a) Find the tensions T1 and T2 in the upper and lower strings in terms of m, a, and g. (b) Compare the two tensions and determine which string would break first if a is made sufficiently large. (c) What are the tensions if the cable supporting the elevator breaks? Figure P4.33 Problems 33 and 34.arrow_forwardAn object of mass M is held in place by an applied force F and a pulley system as shown in Figure P4.43. The pulleys are massless and frictionless. (a) Draw diagrams showing the forces on each pulley. Find (b) the tension in each section of rope, T1, T2, T3, T4, and T5 and (c) the magnitude of F. Figure P4.43 44. Any device that allows you to increase the force you exert is a kind of machine. Some machines, such as the prybar or the inclined plane, are very simple. Some machines do not even look like machines. For example, your car is stuck in the mud and you cant pull hard enough to get it out. You do, however, have a long cable that you connect taut between your front bumper and the trunk of a stout tree. You now pull sideways on the cable at its midpoint, exerting a force f. Each half of the cable is displaced through a small angle from the straight line between the ends of the cable. (a) Deduce an expression for the force acting on the car. (b) Evaluate the cable tension for the case where = 7.00 and f = 100 N.arrow_forwardTwo objects are connected by a light string that passes over a frictionless pulley as shown in Figure P4.30. Assume the incline is frictionless and take m1 = 2.00 kg, m2 = 6.00 kg, and = 55.0. (a) Draw free-body diagrams of both objects. Find (b) the magnitude of the acceleration of the objects, (c) the tension in the string, and (d) the speed of each object 2.00 s after it is released from rest. Figure P4.30arrow_forward
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning