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 39AP
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 39AP
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 39AP
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 39AP
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 39AP
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 39AP
The magnitude
Explanation of Solution
Recall the equation (II).
Substitute
Conclusion:
Therefore, the magnitude
Want to see more full solutions like this?
Chapter 5 Solutions
Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Single-term
- If the vector components of the position of a particle moving in the xy plane as a function of time are x(t)=(2.5ms2)t2i and y(t)=(5.0ms3)t3j, when is the angle between the net force on the particle and the x axis equal to 45?arrow_forwardThe x and y coordinates of a 4.00-kg particle moving in the xy plane under the influence of a net force F are given by x = t4 6t and y = 4t2 + 1, with x and y in meters and t in seconds. What is the magnitude of the force F at t = 4.00 s?arrow_forwardLet us make the (unrealistic) assumption that a boat of mass m gliding with initial velocity v0 in water is slowed by a viscous retarding force of magnitude bv2, where b is a constant, (a) Find and sketch v(t). How long does it take the boat to reach a speed of v0/l000? (b) Find x(t). How far does the boat travel in this time? Let m = 200 kg, v0 = 2 m/s, and b = 0.2 Nm-2s2.arrow_forward
- A ball is falling toward the ground. Which of the following statements are false? (a) The force that the ball exerts on Earth is equal in magnitude to the force that Earth exerts on the ball, (b) The ball undergoes the same acceleration as Earth. (c) The magnitude of the force the Earth exerts on the ball is greater than the magnitude of the force the ball exerts on the Earth.arrow_forwardA person in a kayak starts paddling, and it accelerates from 0 to 0.8 mile/hour in adistance of 0.8km. If the combined mass of the person and the kayak is 80kg, whatis the magnitude of the net force acting on the kayak?arrow_forwardIn a laboratory experiment, an initially stationary electron (mass = 9.11 x 10–31 kg) undergoes a constant acceleration through 2.4 cm, reaching a speed of 5.7 x 106 m/s at the end of that distance. What are (a) the magnitude of the force accelerating the electron and (b) the electron's weight?arrow_forward
- The two barges shown here are coupled by a cable of negligible mass. The mass of the front barge is 2.00 × 103 kg and the mass of the rear barge is 3.00 × 103 kg. A tugboat pulls the front barge with a horizontal force of magnitude 20.0 × 103 N, and the frictional forces of the water on the front and rear barges are 8.00 × 103 N and 10.0 × 103 N, respectively. Find the horizontal acceleration of the barges and the tension in the connecting cable.arrow_forwardIn the figure, block 1 of mass m1 = 1.9 kg and block 2 of mass m2 = 1.4 kg are connected by a string of negligible mass. Block 2 is pushed by force F→ of magnitude 23 N and angle θ = 33°. The coefficient of kinetic friction between each block and the horizontal surface is 0.16. What is the tension in the string?arrow_forwardThree forces act on an object, considered to be a particle, which moves with constant velocity v =(3 m/s)î +(−2 m/s)ĵ Two of the forces are shown in the picture below., while the third force, F_3 is not given. 1.) What are the x, y, and z components of F_3?arrow_forward
- A 3.5 kg particle moves along an x axis according to x(t) = −12 + 5t2 − 4t3, with xin meters and t in seconds. In unit-vector notation, what is the net force acting on theparticle at t = 6 s?arrow_forwardIf a nonzero constant net external force acts on an object during a given period, which of the following statements must be true during that time? a. The object accelerates b. The magnitude of the object's velocity increases c. The acceleration of the object is increasing d. The object movesarrow_forwardWhich of the following statements about friction is not true? * A. An object of large mass is pulled down onto a surface with a greater force than an object of low mass and, as a consequence, experiences a greater friction B. The direction of friction is always opposite to the direction of motion C. Friction is a force D. The direction of friction is always the same as the direction of motionarrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning