Concept explainers
Two blocks of masses m1 and m2, are placed on a table in contact with each other as discussed in Example 5.7 and shown in Figure 5.13a. The coefficient of kinetic friction between the block of mass m1 and the table is μ1, and that between the block of mass m2 and the table is μ2. A horizontal force of magnitude F is applied to the block of mass m1. We wish to find P, the magnitude of the contact force between the blocks. (a) Draw diagrams showing the forces for each block. (b) What is the net force on the system of two blocks? (c) What is the net force acting on m1? (d) What is the net force acting on m2? (e) Write Newton’s second law in the x direction for each block. (f) Solve the two equations in two unknowns for the acceleration a of the blocks in terms of the masses, the applied force F, the coefficients of friction, and g. (g) Find the magnitude P of the contact force between the blocks in terms of the same quantities.
(a)
The free body diagram of each block with forces.
The free body diagram of an object represents the direction and magnitude of forces acting on the body.
Explanation of Solution
The mass of block
The free body diagram of the book is given below.
Figure (1)
The sum of all vertical forces is zero because the block moves on a horizontal surface. So the vertical acceleration,
Write the net force in the y-direction for mass
Here,
Write the net force in the y-direction for mass
Here,
Write the equation for kinetic friction for block
Here,
Write the equation for kinetic friction for block
Here,
In the figure,
Conclusion:
Therefore, the free body diagram of each block to show the forces is given in figure I.
(b)
The net force on the system of two blocks.
Answer to Problem 5.79AP
The net force on the system of two blocks is the external force applied minus the frictional force.
Explanation of Solution
Write the expression for the net force in x-direction for the system of two blocks from the figure I,
Here,
Conclusion:
Therefore, the net force on the system of two blocks is the external force applied minus the frictional force.
(c)
The net force acting on
Answer to Problem 5.79AP
The net force acting on
Explanation of Solution
Write the expression for the net force in x-direction for the system of two blocks from the figure I,
Here,
Conclusion:
Therefore, the net force acting on
(d)
The net force acting on
Answer to Problem 5.79AP
The net force acting on
Explanation of Solution
Write the expression for the net force in x-direction for the system of two blocks from the figure I,
Here,
Conclusion:
Therefore, the net force acting on
(e)
The Newton’s second law in the
Answer to Problem 5.79AP
The Newton’s second law in the
Explanation of Solution
The block has on a horizontal acceleration
Write the Newton’s second law for block
Substitute
Substitute
Write the Newton’s second law for block
Substitute
Substitute
Conclusion:
Therefore, the Newton’s second law in the
(f)
The acceleration of the blocks.
Answer to Problem 5.79AP
The acceleration of the blocks is
Explanation of Solution
Write the Newton’s second law is for block
Write the Newton’s second law is for block
Conclusion:
Add the equation (I) and equation (II) and solve for
Therefore, the acceleration of the blocks is
(g)
The magnitude of the contact force between the blocks in terms of acceleration, mass, applied force and the friction coefficient.
Answer to Problem 5.79AP
The magnitude
Explanation of Solution
Recall the equation (II).
Substitute
Conclusion:
Therefore, the magnitude
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