Question 1 A sheep with a mass (m) 50 kg is hung on an animal scale system which consist of a helical spring of negligible mass. The stiffness (k) of the spring is 60 kN/m. During the hanging operation, the spring and the sheep are displaced vertically by 20 mm below the equilibrium position. 1.1. Draw a free body diagram and proof that a total length (L) of the scale system can be expressed as: L = 2mg + Lo, where as Lo is the unstretched length of k the spring. 1.2. Calculate the frequency of natural vibration of the system. 1.3. Calculate the velocity and acceleration of the sheep when it is 10 mm below the rest position. For question 1.4 and 1.5, indicate whether the statement presented is true or false. If true, state why. If false, rewrite the statement to make it true. 1.4. The differential equation governing the free vibrations of a sliding mass-spring and viscous-damper system (without friction) is the same as the differential equation for a hanging mass-spring and viscous-damper system. 1.5. Springs in series have an equivalent stiffness that is the sum of the individual stiffnesses of these springs.

Question 1 A sheep with a mass (m) 50 kg is hung on an animal scale system which consist of a helical spring of negligible mass. The stiffness (k) of the spring is 60 kN/m. During the hanging operation, the spring and the sheep are displaced vertically by 20 mm below the equilibrium position. 1.1. Draw a free body diagram and proof that a total length (L) of the scale system can be expressed as: L = 2mg + Lo, where as Lo is the unstretched length of k the spring. 1.2. Calculate the frequency of natural vibration of the system. 1.3. Calculate the velocity and acceleration of the sheep when it is 10 mm below the rest position. For question 1.4 and 1.5, indicate whether the statement presented is true or false. If true, state why. If false, rewrite the statement to make it true. 1.4. The differential equation governing the free vibrations of a sliding mass-spring and viscous-damper system (without friction) is the same as the differential equation for a hanging mass-spring and viscous-damper system. 1.5. Springs in series have an equivalent stiffness that is the sum of the individual stiffnesses of these springs.

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter10: Virtual Work And Potential Energy

Section: Chapter Questions

Problem 10.62P: The bar ABC is supported by three identical, ideal springs. Note that the springs are always...

See similar textbooks

Similar questions

The bar ABC is supported by three identical, ideal springs. Note that the springs are always vertical because the collars to which they are attached are free to slide on the horizontal rail. Find the angle at equilibrium if W = kL. Neglect the weight of the bar.
A sheep with a mass (m) 50 kg is hung on an animal scale system which consist of a helical spring of negligible mass. The stiffness (k) of the spring is 60 kN/m. During the hanging operation, the spring and the sheep are displaced vertically by 20 mm below the equilibrium position. 1.1. Draw a free body diagram and proof that a total length (L) of the scale system 2mg can be expressed as: L = k + Lo, where as Lo is the unstretched length of the spring. 1.2. Calculate the frequency of natural vibration of the system. 1.3. Calculate the velocity and acceleration of the sheep when it is 10 mm below the rest position.
Two blocks are connected by a (massless) string that passes over a (massless, frictionless) pulley as shown. Assume the interface between block A and the horizontal tabletop to be frictionless. pulley If mA = 6.3 kg and mg = 8.8 kg, what is the tension in the string? Express your answer in N, to at least one digit after the decimal point.
A bored student builds a levitating lantern using objects they 3D printed in the Fischer Engineering Design Center. The student connects the blue and green pieces with two strings at points A and B, as shown below. If the blue (top) object weighs 181 g and the tension in string A is 3.2 N, what is the distance from the left side of the object to its center of mass in cm? Assume the system is in static equilibrium.
A crate with a mass of 400 kg is held in equilibrium by three ropes attached to a steel ring. B d2 m Variable Value d₁ 2.5 m d₂ 5 m d3 3.5 m d4 3 m d5 2.5 m C da ds Values for the figure are given in the following table. Note the figure may not be to scale. a. Determine the magnitude of the force/tension in cord A, TA. b. Determine the magnitude of the force/tension in cord B, TB. c. Determine the magnitude of the force/tension in cord C, Tc. Round your final answers to 3 significant digits/figures. The magnitude of the force/tension in cord A is N The magnitude of the force/tension in cord B is N The magnitude of the force/tension in cord C is N
A 50 kg pole extends up a wall, making a 60° angle with the wall. The pole is supported by acable attached 3/4 of the way along the pole. This support cable is perpendicular to the wall.A 10 kg sign hangs from the end of the pole. The pole’s center of mass is 1/3 of the way fromthe wall to the end of the pole. (a) What is the tension in the cable?(b) What are the x and y components of the force the wall exerts on the pole?You must include an extended free body diagram showing all forces acting on the pole. Labelthe location on the pole you will use a reference for measuring distances (the “axis of rotation”) at the point where the pole touches the wall. Thank you!
Course Home Syllabus Scores eText Study Area Document Sharing User Settings Course Tools > Problem 3.46 Each spring has an unstretched length of 2 m and a stiffness of k = 330 N/m .(Figure 1) Figure 4 m Во 12 m 6 m 1 of 1 Part A SOA = Determine the stretch in OA spring required to hold the 22-kg crate in the equilibrium position shown. Submit Express your answer to two significant figures and include the appropriate units. Part B 0 .06 P Pearson μA X Incorrect; Try Again m Previous Answers Request Answer
One end of a uniform 2.60m rod with a mass of 38.0kg is supported by a cable connecting one end to the wall so that the cable makes an angle of 42.0° with respect to the rod. The other end rests against the vertical wall, where it is held in place by friction so that the rod is perfectly horizontal. A sign with an unknown mass is hung from the rod 1.90m from the wall so that wall exerts a normal force of 1790N on the rod in the positive x-direction. What is the mass of the sign in kilograms?
Question 2) The figure shows a mechanical model of the Russel fracture traction device and the leg. The leg is held in balance in the position indicated by the two weights attached to the two cables. The combined weight of the leg and the cast is W=210 N. The horizontal distance between points A and B where the cables are attached to the leg is L=100 cm and the vertical distance is d=6 cm. Point C is the center of gravity of the cast and leg at three quarters of the L measured from point A (3L/4= 75 cm). The angle that cable 2 makes with the horizontal is measured as β=33°. Accordingly, in order for the leg to remain in balance in the shown position; a) Find the tensile force T1 in cable 1. (Write your result in N) b) Find the tensile force T2 in cable 2. (Write your result in N) c) Find the angle α of cable 1 with the horizontal. Response
4. A uniform ladder 10m long and weighing 350N rests against a smooth wall at an angle of 30° with the wall. A 700N man stand 6m up from the bottom of the ladder. Find the horizontal force necessary at the base to keep the ladder from slipping. Draw the FBD
A 4.2‑kg brown hare walks on a horizontal beam (the beam's mass m = 2.8 kg and length a = 2.4 m). The beam is suspended with two ropes attached to the ends of the beam. What should be the distance between the hare and the left end of the beam so that the tension in the left rope is three times as big as the tension in the right rope? 1. The distance from the left end, b = If the hare is at the distance found in the previous question, calculate the tension in each rope. 2. The tension in the left rope, T1 = 3. The tension in the right rope, T2 = ------------------------------------------------------------------ A bike wheel has a radius of R = 0.62 m and a mass of m = 2.6 kg spins at 270 rpm. What is the angular momentum of the wheel? Assume that the wheel has a shape of a ring. The angular momentum of the wheel, L ? A typical bowling ball might have a mass of 7 kg and a radius of 12 cm. How fast the ball should spin to have the same angular momentum as the wheel from the…
The structure consists of a spring CD and a solid member ABC with a slot at B. The peg at B fits loosely into the slot at B and can hence be interpreted as a smooth support. The unstretched length of the spring is 80 mm. 50 mm 150 mm 50 mm A D C B k = 600 N/m 1.1 Draw separate free-body diagrams of member ABC and the spring CD. 1.2 Comment on the existence of two-force members and three-force members in this system. 1.3 Determine the reactions at A and B on the member ABC