Determine the force, Mechanical Engineering

Determine the force:

Determine the force P needed to start block B illustrated in Figure moving to the right if the coefficient of friction is 0.3 for all surfaces of contact. Block A weighs 80 N and block B weighs 160 N.

1930_Determine the force.png

Solution

Figure illustrates the free body diagrams for block A and block B. As the possible motion of the block B is towards right, the direction of frictional forces FA & FB are illustrated acting towards left, for block B. While block B moves towards right the relative motion of block A shall be towards left and therefore the frictional force FA for block A is illustrated acting towards right.

Now the conditions of equilibrium may be applied to determine the force P.

For Block A

                                        ∑ Fx  = 0

                             ∴ FA  = T cos 30o  = 0.866 T                                       ------------ (1)

 (where, T is the tension in the given cord)

                                            ∑ Fy  = 0

                                  ∴ N A = WA  - T sin 30o

                                              = 80 - 0.5 T                        -------------- (2)

Also                           FA  = μ N A

                     ∴ 0.866 T = 0.3 (80 - 0.5 T)

 

∴ T = 24/1.016            = 23.62 N                             -------- (3)

 For Block B

∴ FA  = 0.866 × 23.62 = 20.45 N

∴ N A  = 80 - 0.5 × 23.62 N

= 68.19 N

∑ Fy  = 0

∴ N B  = N A  + WB

= 68.19 + 160

= 228.19 N                 ---------- (4)

FB  = μ N B

= 0.3 × 228.19

= 68.46 N

∑ Fx  = 0                   ----------------( 5)

∴ P = FA  + FB

= 20.45 + 68.46

= 88.91 N                    ----------- (6)

Thus, a force 88.91 N is needed to move the block B to the right.

Posted Date: 1/28/2013 5:24:32 AM | Location : United States







Related Discussions:- Determine the force, Assignment Help, Ask Question on Determine the force, Get Answer, Expert's Help, Determine the force Discussions

Write discussion on Determine the force
Your posts are moderated
Related Questions
A plano convex lens of small radius is used

how to prevent absolute noise during meshing of gears

Type of strain: There are basically four type of strain 1. Tensile strain 2. Compressive strain 3. Volumetric strain 4. Shear strain


The specifications for use on a project will be as defined in the Project Execution plan. The Specification requirements will be clarified in the Engineering Estimate or at the Pr

Determine a least square geometric curve y = ax b to the following data : x:  1   2  3   4   5 y: 0.5  2 4.5 8 12.5 Fit a straight line y = a + bx to the following data b

Q. Conceptual engineering phase? During this phase, a conceptual engineering estimate will be prepared by Project Management with input from all disciplines. Activities at t

Write an essay on air, water and soil-based heat pumps. Discuss the advantages and the disadvantages of each system. For each system identify the conditions under which that system

Q.What is Metal working processes? Metal working processes are processes used to produce wrought products. These product include angles, channels, I-beams, round, squar

what is hoop stress