![Engineering Mechanics: Statics & Dynamics (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780133915426/9780133915426_largeCoverImage.gif)
Concept explainers
Determine the unstretched length of DB to hold the 40-kg crate in the position shown. Take k = 180 N/m.
![Check Mark](/static/check-mark.png)
The unstretched length of spring DB.
Answer to Problem 19P
The unstretched length
Explanation of Solution
Given information:
The stiffness of the spring is
The mass of a crate is 40 kg.
Assumption:
Consider the point E in between the points B and C.
Show the free body diagram of the spring as in Figure 1.
Determine the length of the member CD using the formula.
Here, the length of the point DE is
Determine the length of the spring BD using the formula.
Here, the length of the point BE is
Determine the weight of the crate.
Here, the mass of a crate is m and the acceleration due to gravity is g.
Determine the tension force of the member BD and CD by applying the equation of equilibrium.
Along the horizontal direction:
Here, the tension force of the member CD is
Along the vertical direction:
Determine the unstretched length of the spring BD.
Here, the tension force of the spring member BD is
Conclusion:
Substitute 2 m for
Substitute 2 m for
Determine the
Substitute 3 m for
Determine the
Substitute 2m for
Substitute
Substitute 40 kg for m and
Determine the
Substitute 2 m for
Determine the
Substitute 2 m for
Substitute
Substitute 332.96 N for
Substitute 282.96 N for
Thus, the unstretched length of spring DB is
Want to see more full solutions like this?
Chapter 3 Solutions
Engineering Mechanics: Statics & Dynamics (14th Edition)
- The 80-kg crate has its center of gravity at G. Determine the smallest force P that will initiate motion if =35.arrow_forwardDetermine the smallest horizontal force P that would push the homogeneous cylinder of weight W over the curb. Neglect friction.arrow_forwardThe homogeneous bar AB weighs 25 lb. Determine the magnitudes of the forces acting on the bar at A and B. Neglect friction.arrow_forward
- The homogeneous plate of weight W is suspended from two cables. Determine the force P that is necessary to keep the plate in the position shown.arrow_forwardThe cable AOB weighs 24 N/m. Determine the sag H and the maximum tension in the cable.arrow_forwardThe woman is trying to move the crate of weight W by pulling on the rope at the angle to the horizontal. Find the smallest possible tension that would cause the crate to slide and the corresponding angle .arrow_forward
- The homogeneous plate of weight W is supported by a ball-and-socket joint at D and three wires. Draw the FBD of the plate and count the unknowns.arrow_forwardMembers AC and AB support the 100-lb crate. Determine the tensile force developed in member (AB). 3 ft 4 ft 4 ftarrow_forwardQS/ A man stands out at the end of the diving board, which is supported by two springs A and B, cach having a stiffness of . In the position shown the board is horizontal. If the man has a mass of 40 kg, determine the angle of tilt which the board makes with the horizontal after he jumps off. Neglect the weight of the board and assume it is rigid. 1m 3 marrow_forward
- Determine the force P that will keep the pulley system in equilibrium. Neglect the weights of the pulley. 9000 Narrow_forwardFind the minimum force F to cause movement of the 400/1000 lb. system shown. The 5º wedge is weightless. rollers 400 16 66 1000 16 wedg(50) Ms 0.40 X=0.30 rollersarrow_forwardSolve the components of reaction at its support given the compound shown below. Neglect its weight and thickness. Show FBD and complete solutionarrow_forward
- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305501607/9781305501607_smallCoverImage.gif)