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 12.18P
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 zero.
Calculation:
Write the general equation of weight (W):
Here, m is the mass, g is the acceleration due to gravity.
Consider the constraint of cord.
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
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
Find the angle
Equate Equation (5) and (6).
Divide Equation (3) by
Substitute 40 kg for
The angle
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 (8) and (9).
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 12.18P
The tension in the cord is
Explanation of Solution
Calculation:
Find the tension in the cord using Equation (9).
Substitute
Thus, the tension in the cord is
Want to see more full solutions like this?
Chapter 12 Solutions
VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS
Additional Engineering Textbook Solutions
Starting Out with Python (4th Edition)
Thermodynamics: An Engineering Approach
Starting Out with C++ from Control Structures to Objects (9th Edition)
Electric Circuits. (11th Edition)
Automotive Technology: Principles, Diagnosis, And Service (6th Edition) (halderman Automotive Series)
Database Concepts (8th Edition)
- Solve this problem and show all of the workarrow_forwardaversity of Baoyion aculty of Engineering-AIMusyab Automobile Eng. Dep. Year: 2022-2023, st Course, 1st Attempt Stage: 3rd Subject: Heat Transfer I Date: 2023\01\23- Monday Time: 3 Hours Q4: A thick slab of copper initially at a uniform temperature of 20°C is suddenly exposed to radiation at one surface such that the net heat flux is maintained at a constant value of 3×105 W/m². Using the explicit finite-difference techniques with a space increment of Ax = = 75 mm, determine the temperature at the irradiated surface and at an interior point that is 150 mm from the surface after 2 min have elapsed. Q5: (12.5 M) A) A steel bar 2.5 cm square and 7.5 cm long is initially at a temperature of 250°C. It is immersed in a tank of oil maintained at 30°C. The heat-transfer coefficient is 570 W/m². C. Calculate the temperature in the center of the bar after 3 min. B) Air at 90°C and atmospheric pressure flows over a horizontal flat plate at 60 m/s. The plate is 60 cm square and is maintained at a…arrow_forwardUniversity of Baby on Faculty of Engineering-AIMusyab Automobile Eng. Dep. Year: 2022-2023. 1 Course, 1" Attempt Stage 3 Subject Heat Transfer I Date: 2023 01 23- Monday Time: 3 Hours Notes: Q1: • • Answer four questions only Use Troles and Appendices A) A flat wall is exposed to an environmental temperature of 38°C. The wall is covered with a layer of insulation 2.5 cm thick whose thermal conductivity is 1.4 W/m. C, and the temperature of the wall on the inside of the insulation is 315°C. The wall loses heat to the environment by convection. Compute the value of the convection heat-transfer coefficient that must be maintained on the outer surface of the insulation to ensure that the outer-surface temperature does not exceed 41°C. B) A vertical square plate, 30 cm on a side, is maintained at 50°C and exposed to room air at 20°C. The surface emissivity is 0.8. Calculate the total heat lost by both sides of the plate. (12.5 M) Q2: An aluminum fin 1.5 mm thick is placed on a circular tube…arrow_forward
- Solve this and show all of the workarrow_forwardNeed helparrow_forwardY F1 α В X F2 You and your friends are planning to move the log. The log. needs to be moved straight in the x-axis direction and it takes a combined force of 2.9 kN. You (F1) are able to exert 610 N at a = 32°. What magnitude (F2) and direction (B) do you needs your friends to pull? Your friends had to pull at: magnitude in Newton, F2 = direction in degrees, ẞ = N degarrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY