Concept explainers
Review. A block of mass m1 = 2.00 kg and a block of mass m2 = 6.00 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of θ = 30.0° as shown in Figure P10.72. The coefficient of kinetic friction is 0.360 for both blocks. (a) Draw force diagrams of both blocks and of the pulley. Determine (b) the acceleration of the two blocks and (c) the tensions in the string on both sides of the pulley.
Figure P10.72
(a)
Sketch the force diagrams of both blocks and pulley.
Answer to Problem 72P
The free body diagram of the block of mass
The free body diagram of the block of mass
The free body diagram of the pulley is shown below.
Explanation of Solution
Consider the figure of given system
In physics and engineering free body diagrams are used for visualizing the forces, movements, and reaction forces acting on a body. The direction of the forces are also shown in free body diagram using straight arrows.
The free body diagram of the block of mass
The mass
The free body diagram of the block of mass
The mass
The free body diagram of the pulley is shown below.
(b)
The acceleration of two blocks.
Answer to Problem 72P
The acceleration of two blocks is
Explanation of Solution
Consider the free body diagram of mass
Write the expression for the total force acting on mass
Here,
The net force acting in vertical direction will be zero, since the normal force and
Rewrite equation (I).
Write the expression for kinetic friction force on
Here,
Write the expression for the force acting in
Here,
Rewrite equation (IV) including the components of forces in horizontal direction.
Write the expression for the total torque.
Here,
Substitute,
Similarly the net force acting on
Write the expression for the kinetic force of friction acting on mass
Write the expression for the forces acting on
Add equation (V), (VII), and (X)
Substitute, equation (IX) and (III) in (XI),
Conclusion:
Substitute,
Therefore, the acceleration of two blocks is
(c)
The tension in the string on both sides of the pulley.
Answer to Problem 72P
The tension in the string on both sides of the pulley is
Explanation of Solution
Use equation (V) and (VII) to obtain the answer.
Conclusion:
Substitute,
Substitute,
Therefore, the tension in the string on both sides of the pulley is
Want to see more full solutions like this?
Chapter 10 Solutions
Principles of Physics: A Calculus-Based Text
- The puck in Figure P11.46 has a mass of 0.120 kg. The distance of the puck from the center of rotation is originally 40.0 cm, and the puck is sliding with a speed of 80.0 cm/s. The string is pulled downward 15.0 cm through the hole in the frictionless table. Determine the work done on the puck. (Suggestion: Consider the change of kinetic energy.) Figure P11.46arrow_forwardA block of mass m, = 2.45 kg and a block of mass m, = 5.65 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of e = 30.0° as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks. Use g=9.8 m/s2. М, R m2 (b) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.) m/s2 (c) Determine the tensions in the string on both sides of the pulley. left of the pulley N right of the pulley Narrow_forwardI'm struggling to understand how to do this: A block of mass m1 = 1.55 kg and a block of mass m2 = 6.05 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of θ= 30.0°. The coefficient of kinetic friction is 0.360 for both blocks. Use g=9.8 m/s2. (a) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.) (b) Determine the tensions in the string on both sides of the pulley (left side and right side).arrow_forward
- You have a cylinder. You don't know what its internal structure looks like, but you plan to roll it down a ramp, as in this week's procedure. The ramp is 1 m long, and is elevated at an angle of 15°. The mass of the cylinder is 450 g and its diameter is 2.1 cm.After you release the cylinder, it rolls down the ramp without slipping, gaining speed. How much total energy (in J)does the block have at the bottom of the ramp?arrow_forwardThe engine of the bus applies a torque of 533 N · m to a wheel of radius 0.2 m. Since the wheel does not slip, the road must be applying a force of static friction to the wheel that produces a counter-torque. Moreover, the bus has a constant velocity, so this counter-torque balances the applied torque. What is the magnitude of the static frictional force?arrow_forwardA solid cylinder (LaTeX: I\:=\frac{\:1}{2}MR^2 I = 1 2 M R 2 ) potter's wheel is a thick stone of radius 7 m with mass 5 kg. It freely rotates at 9 radian per second. The potter press a wet rag against the rim and exert a radially inward force of 10 N. If the coefficient of kinetic friction between the rag and the wheel is 0.6, find the time needed for the wheel to stop in seconds.arrow_forward
- A 24 g block sits at the center of a turntable that rotates at 80 rpm. A compressed spring shoots the block radially outward from the center along a frictionless groove in the surface of the turntable. Calculate the turntable's angular speed when the block reaches the outer edge. Treat the turntable as a solid disk with mass with mass 200 g and diameter 54.0 cm. Express your answer in revolutions per minute.arrow_forwardA uniform rod is set up so that it can rotate about an axis at perpendicular to one of its ends. The length and mass of the rod are 0.765 m and 1.27 kg respectively. A force of constant magnitude ?F acts on the rod at the end opposite the rotation axis. The direction of the force is perpendicular to both the rod's length and the rotation axis. Calculate the value of ?F that will accelerate the rod from rest to an angular speed of 6.21 rad/s in 9.91 sarrow_forwardA 8.10 kg uniform disk with a radius of 14.3 cm is wrapped with a massless string and is suspending a 4.47 kg mass. What is the tension in the string as the mass falls? What is the speed of the mass after it has fallen 3.56 m?arrow_forward
- A block of mass m, = 1.90 kg and a block of mass m, = 6.35 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of 0 = 30.0° as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks. М, R (a) Draw force diagrams of both blocks and of the pulley. Choose File No file chosen This answer has not been graded yet. (b) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.) |m/s² (c) Determine the tensions in the string on both sides of the pulley. left of the pulley right of the pulleyarrow_forwardA block of mass m, = 1.55 kg and a block of mass m, = 5.65 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge- shaped ramp makes an angle of 0 = 30.0° as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks. М, R (a) Draw force diagrams of both blocks and of the pulley. Choose File No file chosen (b) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.) m/s2 (c) Determine the tensions in the string on both sides of the pulley. left of the pulley N right of the pulleyarrow_forwardA block of mass m, = 1.55 kg and a block of mass m, = 6.25 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of 0 = 30.0° as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks. М, R m1 (a) Draw force diagrams of both blocks and of the pulley. Choose File No file chosen This answer has not been graded yet. (b) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.) m/s2 (c) Determine the tensions in the string on both sides of the pulley. left of the pulley 6.04 right of the pulley Narrow_forward
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author: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: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning