Concept explainers
Block A has a mass of 10 kg, and blocks B and C have masses of 5 kg each. Knowing that the blocks are initially at rest and that B moves through 3 m in 2 s, determine (a) the magnitude of the force P, (b) the tension in the cord AD. Neglect the masses of the pulleys and axle friction.
Fig. P12.28
(a)
Find the magnitude of the force P.
Answer to Problem 12.28P
The magnitude of the force P is
Explanation of Solution
Given information:
The mass of block A
The mass of blocks B
The mass of blocks C
The initially block B
The distance of movement for block B
The time taken by block B to move 3 m (t) is 2 s.
Calculation:
Sketch the system with position of blocks as shown in Figure 1.
Write the general equation of weight (W):
Here, m is the mass, g is the acceleration due to gravity.
Refer Figure (1).
Consider the position of y be positive downward.
Consider the constraint of cord AD.
Write total length of cable connecting block A and block D.
Here,
Differentiate Equation (1) with respect to t to write velocity of the blocks.
Here,
Differentiate Equation (2) with respect to t to write acceleration of the blocks.
Here,
Consider the constraint of cord BC.
Write total length of cable connecting block A and block D.
Here,
Differentiate Equation (4) with respect to t to write velocity of the blocks.
Here,
Differentiate Equation (5) with respect to t to write acceleration of the blocks.
Here,
Substitute
The motion of blocks is uniform.
Find the acceleration of block B
Here,
Substitute
Substitute 3 m for
Sketch the free body diagram of pulley D as shown in Figure 2.
Refer Figure (2),
Consider equilibrium along y-axis.
Here,
Sketch the free body diagram of block A as shown in Figure (3).
Apply Newton’s law of motion along y-axis.
Here,
Substitute
Sketch the free body diagram of block C as shown in Figure (4).
Refer Figure (4),
Apply Newton’s law of motion along y-axis.
Here,
Substitute
Find the tension in the cord BC using Equation (7).
Substitute
Substitute 10 kg for
Sketch the free body diagram of block B as shown in Figure (5).
Refer Figure (5),
Find the magnitude of the force P.
Apply Newton’s law of motion along y-axis.
Here,
Substitute
Substitute 5 kg for
Thus, the magnitude of the force P is
(b)
Find the tension in the cord AD.
Answer to Problem 12.28P
The tension in the cord AD is
Explanation of Solution
Calculation:
Find the tension in the cord AD using Equation (8).
Substitute
Thus, the tension in the cord is
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