Two massless springs, each with a spring constant of k, are used in an experiment. Spring 1 is attached to a ceiling while spring 2 is vertically attached to a table. A mass (m) is hung from spring 1 while an identical mass is placed on top of spring 2. Which spring will exert a greater force magnitude on the respective mass once the spring/mass systems reach equilibrium? A. Spring 1 B. Spring 2 C. They exert the same force magnitude. D. It depends upon the magnitude of the mass.
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- Question 1 (Type B) Given the figure shown below, what is the mass of block B on the smooth incline if the system is in static equilibrium? A spring, with a spring constant of 300 N/m and resting length of 1.5 m, runs from block B up to A. B 40° 1m A 1.5 mPart (A)- In a Hartnell governor, the mass of each ball is 6 kg. The lengths of ball arm and sleeve arm of each bell crank lever are 120 mm and 100 mm respectively. The minimum radius of rotation of governor ball is 90 mm. If the controlling forces are 1200 N and 600 N corresponding to 175 mm and 100 mm radius of rotation of governor balls respectively, find the initial compression of spring required.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 2mg can be expressed as: L = + 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…
- 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.1. The PASCO human arm model is configured such that the cord representing the bicep is perfectly vertical and the forearm is at 90° (in the figure to the right, the cord is not quite vertical). A mass of 100 g is attached to the hand. Draw a free-body diagram on the figure to the right showing all forces which act on the forearm. The force of the bicep F on the arm The force of the humerus FH on the arm The weight of the forearm W The mass in the hand Wm 100 g Be careful to draw the force vectors with tails beginning at the point where the force is actually applied to the forearm. 2. Consider the free body diagram below. Determine the perpendicular component F̟ of the force F exerted by the biceps brachii on the forearm. Use the fact that cos 0 = H/B to write this component directly in terms of the humerus length H and the biceps length B. H 3. If the forearm is in equilibrium, then there is no angular acceleration and therefore the sum of the torques applied to the forearm must be…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?
- I need your help expert. The system shown below is in equilibrium. Spring 3 is known to have a change in length of 10 cm. The magnitude of the compressive force in Spring 2 is 15% more than the magnitude of force P, while the magnitude of the compressive force in Bar 1 is 100 N less than that in Spring 2. If the spring constants of Springs 2 and 3 are 625 and 1200 N/m, respectively, determine the following: a. magnitude of forces P (in N) and F (in N) b. tension (in N) in cable ABC c. mass (in kg) of Block A d. compressive force in Bar 1 e. change in length (in cm) of Spring 2 Draw the complete FBD’s of Block A, Hook C and Pulley E. (Note: Below are the final answers, kindly match your answer on this. Thank you) Answer: P = 131.2831 N, F = 87.1569 N, TABC = 110.7024 N, mA = 15.6338 kg, F1 = 50.9756 N, s2 = 24.1561 cmortal X + kent.ac.uk/2021/pluginfile.php/680076/mod_resource/content/1/EENG3230_2022.pdf 4- Question 3 Two blocks, A and B, of mass m and 3m respectively, are connected through a cable and a pulley (see figure 3.1). Block A is also attached to a spring, which is fixed to the ground and has a spring constant k = 50 N/m. Block B is on an inclined plane forming an angle of 30 degrees with the horizontal line. Block B is released from rest with no slack in the cable and with the spring not being stretched or compressed. Assign to m the value in kg of your body weight, then (a) calculate the distance covered by block B once it stops for the first time; assume that there is no friction. (b) assume a kinetic friction force F = 5 N acts on block B and calculate the distance covered by block B once it stops for the first time. State any assumptions and comment on your solutions. B 3m £ F3 F4 Q DII % F5 ☀ 30° F6 H F7 PrtScn F8 WWW 8 (0 Home F9 W End F10 PgUp F11 PgDn C F12The system shown is in static equilibrium and motionless. • The force "P" is at the maximum magnitude that will not initiate motion. NOTE: Submitted responses shall be to 4 significant figures. Do NOT use scientific notation. Find: 1. The magnitude of weight of Block-A is 2. The magnitude of internal force in the rope is N. _N. 3. The magnitude of normal force between Block-A and Block-B is N. 4. The magnitude of friction force between Block-A and Block-B is N. 5. The magnitude of normal force between Block-B and the Ground is 6. The magnitude of friction force between Block-B and the Ground is 7. The magnitude of force P is_N. _N. N. A 100 kg 30° H, = 0.30 200 kg B P -Hy = 0.20
- III. Equilibrium of Non-Concurrent Force System 1. Weight lifter Hidilyn Diaz made a history becoming the first atlete from the Philippines to win gold at the Olympics. She competed in the women's 55 kg weightlifting competition during the Tokyo 2020 Olympic Games at the Tokyo International Forum in Tokyo on July 26, 2021. She lifted a barbell with the total weight of 127 kg comprising of weight of plates: W1 = 50 kg, W2 = 6 kg; and standard weight of the olympic bar, W3 = 15 kg where it is located at the centroid of the bar. The standard length of women's olympic bar is 2.01 meters. As long as she is holding the barbell above her head, both bodies (weighlifter and barbell) are in static equilibrium. What are the forces, R1 and R2 exerted by her arms to keep her in static equilibrium? Assume the olympic bar is rigid. 2 O10 mm 1420mm 90mm To mm 320 mm 320 m 68 R2 65 R, W, Wi PHILIPPINESb. A 50 kg block is supported by the spring arrangement shown in Fig. 4b i. ii. iii iv. 12 kN/m www www 24 kN/m 50 kg wwww 12 kN/m Fig. 4b Sketch the free body diagram for: The static equilibrium position for the system; The dynamic case when the mass is displaced downwards by a deflection of x m and released. The 50 kg block in Fig. 4b (above) is moved vertically downward from its equilibrium position and released and it then vibrates in simple harmonic motion (SHM). Knowing that the amplitude of the resulting motion is 40 mm, determine the following: Frequency of vibration in Hz; Maximum velocity of the block.Q3: For the equilibrium position shown 4 ft 4 ft in fig. (2), 0 = 43°. Find the mass (m) of the lamp fixture suspended from the two springs, if each spring has an unstretched wwww k= 5 lb/ (before the equilibrium) length of 4 ft and k- 5 lb/t stiffness of k = 5 Ib/ft. (lamp fixture) W of lamp fixture Fig. (2)