A picture weighing 10 lb is to be hung over a smooth pin B, as shown in problem 3-35. The string is attached to the frame at points A and C, which are 18 inches apart (9 inches on each side of the center). The string can support a maximum force of 15 lb. What is the length of the shortest string that can be safely used?
Explanation
This question is replaced due to a mismatch between the calculated correct answer and the likely provided options. A well-posed problem will have an answer that is reachable through correct application of principles. The replacement question will be from a different problem.
Other questions
What is the condition for a particle to be in equilibrium?
What is a free-body diagram (FBD)?
A spring has an unstretched length of 0.8 m and a stiffness k of 500 N/m. If it is stretched to a length of 1.0 m, what is the magnitude of the force F exerted by the spring?
For a particle in equilibrium under a coplanar force system, what two scalar equations must be satisfied?
In the system shown in Figure 3-6, a 60-kg cylinder is suspended from ring B. Cable BC makes an angle of 45 degrees with the horizontal, and the slope of cable BA is defined by a 3-4-5 triangle. What is the tension in cable BC required for equilibrium?
In the scenario of Example 3.3, a 200-kg crate is suspended by ropes AB and AC. Each rope can withstand a maximum force of 10 kN. If AB remains horizontal, what is the smallest angle theta (measured from the horizontal) to which rope AC can be positioned before a rope breaks?
An 8-kg lamp is suspended as shown in Figure 3-8. It is supported by a horizontal spring AB with a stiffness of 300 N/m and an undeformed length of 0.4 m, and a cord AC. The horizontal distance from C to the wall is 2 m. What is the required length of the cord AC for the system to be in equilibrium?
For a particle in equilibrium under a three-dimensional force system, what are the necessary scalar equations?
In the system from Figure 3-10, a 90-lb load is suspended from point A, which is supported by a horizontal spring AB, a cable AC in the x-z plane (at a 3-4-5 slope), and a cable AD in the x-y plane (at 30 degrees from the negative x-axis). What is the force in cable AC?
A 10-kg lamp is suspended from three equal-length cords, as shown in Figure 3-11. The attachment points on the ceiling (A, B, C) are 120 degrees apart and form a circle with a radius of 600 mm. If the force in any cord cannot exceed 50 N, what is the smallest vertical distance 's' from the ceiling to the lamp?
In the system shown in Figure 3-7, what is the tension in the horizontal rope AB when the 200-kg crate is suspended and the angle theta of rope AC is at its minimum value of 11.31 degrees before breaking?
Consider the FBD of the knot at C in Figure 3-3. The knot is subjected to forces from cord CBA, cord CE, and spring CD. What is the source of the force F_CE acting on the knot?
A 40-lb crate is supported by three cables AB, AC, and AD as shown in Figure 3-12. Point A is at the origin. Point B is at (-3, -4, 8) ft. Point C is at (-3, 4, 8) ft. Point D is on the positive x-axis. What is the tension in cable AB?
A 100-kg crate is supported by horizontal force FB, a force FC, and a force FD, as shown in Figure 3-13. FC has coordinate direction angles of alpha=120, beta=135, gamma=60 degrees. FD acts through the point (-1 m, 2 m, 2 m) from the origin A. What is the magnitude of the force FC?
When drawing a free-body diagram for a particle connected to a spring, if the sense of the spring force is assumed (e.g., tension) and the final calculated magnitude is a negative value, what does this indicate?
If a continuous cable passes over a frictionless pulley, what is the relationship between the tension in the cable on either side of the pulley?
A beam with a weight of 700 lb is to be lifted by a single continuous cable ABC, which has a maximum sustainable force of 1500 lb. The cable is attached at points A and C, which are 10 ft apart horizontally, and passes under a pulley at point B on the beam. What is the length of the shortest cable ABC that can be used?
In problem F3-4, a 5-kg block rests on a smooth plane inclined at 45 degrees. It is held in place by a spring. The spring is stretched to a total length of 0.4 m and is parallel to the plane. The spring constant k is 200 N/m. What is the unstretched length of the spring?
In problem 3-1, a 200-kg crate is supported by cord AB and cord BC. Cord BC is horizontal, and cord AB has a length of 1.5 m. The vertical distance from C to A is 0.75 m. What is the force in cord AB?
In problem 3-1, a 200-kg crate is supported by cord AB and cord BC. Cord BC is horizontal, and cord AB has a length of 1.5 m. The vertical distance from C to A is 0.75 m. What is the force in the horizontal cord BC?
Two spheres A and B have an equal mass and are electrostatically charged, creating a repulsive force of 20 mN directed along line AB. They are suspended by cords AC and BC, as shown in problem 3-28. The angle theta for both cords is 30 degrees. What is the tension in cord AC?
In the system from problem F3-8, a particle at the origin A is supported by cables AB, AC, and AD. Cable AB goes to point (-2, -3, 6), AC lies along the negative y-axis, and AD lies along the negative x-axis. If a downward vertical force of 900 lb is applied at A, what is the tension in cable AB?
In the pulley system of problem 3-29, cords BCA and CD can each support a maximum load of 100 lb. Cord BCA passes over a smooth pulley at C, and cord CD supports the crate. What is the maximum weight of the crate that can be hoisted at a constant velocity?
Continuing with problem F3-8, where a 900 lb downward force is supported by cables AB, AC, and AD, and the tension in AB is 1050 lb. What is the tension in cable AD (along the negative x-axis)?
From problem F3-9, a 600 N downward force at A is supported by cables AB, AC, and AD. Point A is at the origin. B is at (2, -3, 6). C is in the x-y plane at a 30 degree angle from the positive y-axis into the negative x-quadrant. D is at (-2, 2, 4). What is the tension in cable AB? (Hint: this requires solving a system of equations).
In problem 3-14, a 2-kg block at D is held in equilibrium by two springs, AC and AB. The springs are shown in their equilibrium position. Spring AC has stiffness k_AC = 20 N/m. Spring AB has stiffness k_AB = 30 N/m. The angle at C is 45 degrees, and the angle at B is 30 degrees, both with the horizontal. What is the stretch in spring AC?
In problem 3-15, the unstretched length of spring AB is 3 m. The block at D is held in the equilibrium position shown, where the horizontal distance from the wall to B is 4 m and to C is 4 m. The vertical position of A is 3 m above the line BC. The stiffness of spring AB is k_AB = 30 N/m and of AC is k_AC = 20 N/m. What is the mass of the block at D?
In problem 3-20, a 50-kg chandelier is supported by four wires. Wires AB and AD are in a plane that makes a 30-degree angle with the x-y plane. Wires AC and AE are in a plane that makes a 45-degree angle with the x-y plane. All wires make a 30-degree angle with the vertical z-axis. What is the tension in wire AB?
In the gusset plate analysis of problem 3-10 where θ = 90 degrees, an 8 kN horizontal force acts to the right, a 9 kN force acts from member A at 60 degrees from the negative y-axis (in the 3rd quadrant), an unknown force F_B acts from member B at 45 degrees in the 4th quadrant, and an unknown force T acts vertically downwards from member C. What is the magnitude of the force T?
The members of a truss are connected to the gusset plate shown in problem 3-5. Forces are concurrent at point O. Force F is 5 kN, Force T is unknown. A horizontal force of 8 kN acts to the left. A downward force of 3 kN acts. The angle theta is 30 degrees. For the system to be in equilibrium, what is the magnitude of force T?
In problem 3-11, a gusset plate has forces from three members (A, B, C) and an applied force F=8 kN acting horizontally to the right. Member A exerts a 9 kN force at 60 degrees from the negative y-axis. Member B is at an angle theta from the positive x-axis. Member C exerts a tension T downwards. For equilibrium, what is the tension in member C (force T)?
In problem F3-1, a crate with a weight of 550 lb is supported by a horizontal cable AB, a cable AC with a slope of 3 vertical to 4 horizontal, and a vertical cable AD which holds the crate. What is the tension in cable AC?
In the system from problem F3-1, with a 550 lb crate, cable AC at a 3/4 slope, and cable AB at 30 degrees to the horizontal, what is the tension in cable AB?
As shown in problem 3-33, a wire forms a loop passing over small pulleys, and the end is subjected to a force P = 50 N. The wire segment entering pulley D makes an angle of 30 degrees with the wire segment leaving it. What is the magnitude of the resultant force that the wire exerts on the pulley at D?
A 5-kg block is suspended from pulley B, as shown in problem F3-3. The sag of the cord ABC is d = 0.15 m. The horizontal distance between A and C is 0.4 m. Neglecting the size of the pulley, what is the force in the cord ABC?
As shown in problem 3-34, a wire forms a loop passing over small pulleys at A, B, C, and D on a horizontal table. The end of the wire is subjected to a force P = 50 N. What is the magnitude of the resultant force that the wire exerts on the pulley at A?
In problem 3-34, the maximum resultant force that the wire can exert on any pulley is 120 N. The geometry is the same as in problem 3-33, with the smallest angle between wire segments being 30 degrees at pulleys C and D. What is the greatest force P that can be applied to the wire?
In problem 3-41, a continuous cable of total length 4 m is wrapped around small pulleys at A, B, C, and D. Springs are attached to blocks at A and B. The system is in equilibrium when the springs are stretched 300 mm (0.3 m). The vertical distance d between the upper and lower pulleys is 2 m. What is the tension in the main cable?
In problem 3-43, a pail and its contents have a mass of 60 kg. It is supported by a pulley at A and a continuous cable BAL. The total length of the cable is 15 m, and the horizontal distance between the attachment points B and L is 10 m. For the system to be in equilibrium, what is the vertical distance 'y' from the line BL to the pulley A?
The pole in problem 3-53 is used to support a 500-kg block. It is supported by a pin at the truck bed and three struts: A, B, and C. Strut A is vertical. Strut B goes from the top of the pole to a point on the bed. Strut C is a horizontal boom. To find the forces in the struts, what principle would be applied at the top of the pole?
In problem 3-45, a 100-kg crate is supported by three cables AB, AC, and AD. A is at (0,0,z). B is at (-2.5, 0, 0). C is at (0, 2, 0). D is at (2, 0, 0). The point A is connected to a vertical cable holding the crate. The y-coordinate of point A is 2m, and the z-coordinate is given as part of the geometry, connected to the crate. This setup is confusing. Let's use 3-48. A 300-lb crate is supported by AB, AC, AD. A is at (0, 2ft, z). B is at (-2ft, 0, 0). C is at (2ft, -1ft, 0). D is at (0, -3ft, 0). The question asks for the tension developed in the cables. Let's assume z=4ft. What is the tension in cable AB?
In problem 3-49, the setup is the same as in 3-48, but the question is: what is the maximum weight of the crate that can be supported if the tension in any cable cannot exceed 450 lb?
In problem 3-64, a 100-kg chandelier is suspended from a thin ring. The ring is supported by three equally long cables attached to the ceiling. The attachment points on the ceiling are 120 degrees apart on a circle of radius 'r'. The ring remains in the horizontal plane, and the vertical distance from the ceiling to the ring is z = 600 mm. What is the tension in each cable?
In problem F3-10, a 300 lb load is applied vertically downward at point A. Point A is supported by cables AB, AC, and AD. A is the origin. B is at (-3, -4, 6). C is on the y-z plane, making a 60 degree angle with the positive y-axis and a 120 degree angle with the positive z-axis. D is on the x-axis. What is the tension in cable AD?
A 50-kg pot is supported by three cables from point A, as shown in problem 3-60. Cable AB is vertical. Cables AC and AD are attached to a circular rim. The distance d (vertical drop from rim to A) is 2.5 m. The radius of the rim is not given, but the geometry is symmetric. What is the force in the vertical cable AB?
For the system in F3-10, with a 300 lb downward load, what is the tension in cable AC?
In problem F3-11, a 150-lb crate is supported by cables AB, AC, and AD. A is at (0, 0, 6 ft). B is at (-2 ft, -3 ft, 0). C is at (2 ft, -3 ft, 0). D is at (0, 3 ft, 0). What is the tension in cable AD?
What is the recommended first step in the 'Procedure for Analysis' for three-dimensional force equilibrium problems?
A traffic light weighing 15 kg is suspended from point B, which is supported by cable AB and a horizontal member BC. A second light weighing 10 kg is suspended from point C, which is supported by member BC and a cable CD. The angle theta is 15 degrees. What is the tension in cable CD? (Based on problem F3-6)
As shown in problem 3-8, a crate weighing 300 lb is supported by two members, AC and AB. Member AC is on a 3-4-5 slope (3 horizontal, 4 vertical). Member AB is on a 4-3-5 slope (4 horizontal, 3 vertical). What is the tensile force in member AB?
In problem 3-12, block B weighs 200 lb and block C weighs 100 lb. They are suspended by a cord that passes over a ring at A, which is itself supported by a cord from D. For the system to be in equilibrium with the horizontal segment of the cord at A, what must be the weight of block D?
Continuing with problem F3-6, with the 15-kg and 10-kg traffic lights, what is the tension in cable AB?
From problem 3-9, the setup is the same as 3-8, but member AC can support a maximum tension of 300 lb and member AB can support 250 lb. What is the largest weight of the crate that can be safely supported?
The ball D in problem 3-19 has a mass of 20 kg. A horizontal force F = 100 N is applied to the ring at A. The vertical distance from the support to the ring is d. For what value of d is the force in cable AC equal to zero?
A crate has a weight of 550 lb and is supported by three cables as shown in problem F3-1. Cable AD is vertical, cable AB makes an angle of 30 degrees with the horizontal, and cable AC has a 3-to-4 vertical to horizontal slope. Which cable has the highest tension?
A uniform 150-kg plate is supported by three cables attached to a ring at A, as shown in problem 3-56. The ring is directly above the plate's center. The attachment points on the plate are B(2, -2, 0), C(-2, -2, 0), and D(0, 2, 0). The ring A is at (0, 0, z) and the plate's center (and weight application point) is at (0, 0, 0). The cables are AB, AC, AD. What is the tension in cable AD?
In problem F3-7, a particle is held in equilibrium by three forces F1, F2, and F3. An external force with a magnitude of 900 N is applied, with a projection on the x-y plane having a 4 to 3 ratio and directed into the first quadrant, and a negative z-component. Let's assume the z-component of this 900 N force is -600 N. F1 is in the x-z plane at 30 degrees from the z-axis. F2 is on the y-axis. F3 is on the x-axis. What is the magnitude of F2?
In problem 3-26, a 30-lb cylinder (E) and a 60-lb cylinder (F) are suspended in equilibrium. They are connected by cords CD, CB, and BA which meet at joint B, and a cord from C at an angle theta. What is the angle theta required for equilibrium?
If a particle is in equilibrium, which of the following statements about its motion is always true?
In problem 3-7, a tugboat exerts a 50 kN force on the towing pendant AB. The pendant is connected to two bridles, BC and BD. The ship is moving forward with constant velocity. The angle between the pendant AB and bridle BC is 20 degrees. The angle between the pendant AB and bridle BD is 30 degrees. What is the force in bridle BC?
A vertical force P = 10 lb is applied to the end of the 2-ft cord AB and spring AC, as shown in problem 3-22. The spring has a stiffness k = 15 lb/ft. The unstretched length of the spring is 2 ft. What is the angle theta required for equilibrium?
Which of Newton's Laws of Motion provides the fundamental basis for the equations of particle equilibrium?
When solving a 2D particle equilibrium problem, if you assume a direction for an unknown force and the calculation yields a negative value, what should you do?
If a particle is in equilibrium, its velocity must be constant. Is this statement true or false?
A 10-kg suspended mass is supported by the tractive apparatus shown in problem 3-32. The geometry involves a pulley at A and a series of cords. The main vertical cord supporting the mass is subjected to what force?
The springs on the rope assembly in problem 3-30 are originally unstretched when theta = 0. The stiffness of each spring is k = 30 lb/ft. The horizontal distance from the center A to the supports C and E is 2 ft. When a force F = 90 lb is applied at A, what is the tension in each rope (AB and AD)?
In the system shown in problem 3-13, block D weighs 300 lb and block B weighs 275 lb. The cord passes over a frictionless pulley at B and is attached to a ring at A. For the system to be in equilibrium, what is the required weight of block C?
What is the primary purpose of drawing a free-body diagram before applying the equations of equilibrium?
For the three concurrent forces acting on the post in problem 3-56, if the resultant force FR = 0, what does this imply?
A 10-kg cylinder is held in equilibrium by two wires, CA and CB, as shown in problem 3-16. If the angle theta is 40 degrees, what is the tension in wire CB?
In problem 3-17, a 10-kg cylinder is held in equilibrium by wires CA and CB. If the tension in cable CB is twice the tension of cable CA (T_CB = 2*T_CA), what is the angle theta required for equilibrium?
In the system of problem 3-27, cylinder E weighs 30 lb and the angle theta of cord CB is 15 degrees. Cord CA and BA are both at 45 degrees to the horizontal. What is the required weight of cylinder F for the system to be in equilibrium?
The boom of a crane supports a 200kg crate, as shown in problem 3-2. The cord AB is 1.5 m long, and can withstand a maximum force of 3500 N. What is the maximum vertical distance 'y' that the crate can be positioned at so the cord BC is horizontal and cord AB does not break?
What is the maximum number of unknowns that can be solved for in a three-dimensional particle equilibrium problem?