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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
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Chapter 10 Solutions
Principles of Physics: A Calculus-Based Text
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