Concept explainers
Block A has a mass of 40 kg, and block B has a mass of 8 kg. The coefficients of friction between all surfaces of contact are μs = 0.20 and μk = 0.15. If P = 0, determine (a) the acceleration of block B, (b) the tension in the cord.
Fig. P12.18 and P12.19
(a)
Find the acceleration of block B.
Answer to Problem 12.19P
The acceleration of block B is
Explanation of Solution
Given information:
The mass of block A
The mass of block B
The coefficient of static friction between all surfaces of contact
The coefficient of kinetic friction between all surfaces of contact
The horizontal load (P) is 40 N.
Calculation:
Write the general equation of weight (W):
Here, m is the mass, g is the acceleration due to gravity.
Consider the constraint of chord.
Write total length of cable connecting block A and block B.
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,
Find the equation of acceleration of block B in terms of acceleration of block A.
Here,
Substitute
First of all determine whether the blocks will move for the given value of
Sketch the free body diagram of block B as shown in Figure 1.
Refer Figure (1),
Consider equilibrium along y-axis .
Here,
Substitute
Write the equation of frictional force
Substitute 0.20 for
Consider equilibrium along x-axis.
Substitute
Substitute 8 kg for
Sketch the free body diagram of block A as shown in Figure (2).
Refer Figure (2).
Consider equilibrium along y-axis.
Here,
Substitute
Write the equation of frictional force
Substitute 0.20 for
Consider equilibrium along x-axis.
Substitute
Substitute 40 kg for
Find the force P for impending motion.
Equate Equation (5) and (6).
The force P of impending motion is less than the
Sketch the free body diagram and kinetic diagram of block B as shown in Figure (3).
Refer Figure (3),
Consider equilibrium along y-axis .
Substitute
Write the equation of frictional force
Substitute 0.15 for
Apply Newton’s law of motion along x-axis.
Substitute
Substitute 8 kg for
Sketch the free body diagram and kinetic diagram of block A as shown in Figure 4.
Refer Figure (4).
Consider equilibrium along y-axis.
Substitute
Write the equation of frictional force
Substitute 0.15 for
Apply Newton’s law of motion along x-axis.
Substitute
Substitute 40 kg for
Find the acceleration of block B
Equate equation (7) and (8).
Negative sign indicates the motion of block B in opposite to x-axis.
Thus, the acceleration of block B is
(b)
Find the tension in the cord.
Answer to Problem 12.19P
The tension in the cord is
Explanation of Solution
Calculation:
Find the tension in the cord using Equation (8).
Substitute
Thus, the tension in the cord is
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