help please 3. Two masses m, and m, are situated in a system with ideal pulleys as shown in thefigure. This system is in the vertical plane. A spring (constant k, rest length &)connects mass m: with the ground.Data: m;= 1.5 kg, m2 = 2 kg, m3= 1.5 kg, k = 50 N/m, 6 = 0.4 m, h= 2 m.a) The system is in rest at t = 0s. Determine at that instance the tension in allthe ropes and the compression/extension of the spring.b) Then, an extra mass ms is dropped from a height h, hits mass m2 and sticks tothat mass. During this very short impact, the spring does not exert an impulse.Determine the velocities of all the masses in the system right after the impactand also the impulses exerted by the ropes.c) How much energy was lost during the impact?d) Determine the accelerations of all the masses right after the impact.Solution:1. Make FBD's for m, and for m2 and use theequations of motion (Newton's laws) for eachmass. Projected on a vertical axis, the accelerationsmust be zero.2. Analyse the pulleys: you will find that there isa relation between the forces in the ropes. Thisgives you enough equations to calculate the tension(forces) in the ropes and the spring force. From thelatter, you can calculate the spring extension.3. Use conservation of energy on mass mą tocalculate, using the height h, the velocity of thismass right before it hits the mass m2.Use twice the principle of impulse andmomentum: once for the system of masses m2 +m3 together and once for mass m, each timeprojected on the vertical axis (there is noconservation of momentum, as the ropes apply animpulse on the masses)a. The relation between the tension in thedifferent ropes, obtained in 2, will also determinethe relation between the different impulses of them4.m.m,k, lropes.b. The analysis of the pulleys will also give a relation between theaccelerations and velocities of the masses m: and (m2 + m3).c. From those four equations, you can calculate the impulses of the ropesand the velocities of the masses immediately after the impact.5. Use the work-energy principle (not conservation!) for the entire system(hence all three masses together) to calculate the difference between thekinetic energy before and after the impact, to calculate the loss of energy.6. Make a FBD for the masses m, and (m2 + m3) and write down theequations of motion (Newton's laws) in the vertical direction. Thespring is still as much extended as immediately before the impact (theimpact was very short and hence the spring could not change length inthat time period). The relations between forces and accelerations of thedifferent masses have been obtained previously. Hence you have fourequations and four unknowns (Sı, S2+3, a1, az+3), so you can calculatethese values.

Name: help please 3. Two masses m, and m, are situated in a system with idea
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Description: help please 3. Two masses m, and m, are situated in a system with ideal pulleys as shown in thefigure. This system is in the vertical plane. A spring (constant k, rest length &)connects mass m: with the ground.Data: m;= 1.5 kg, m2 = 2 kg, m3= 1.5 kg,

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Two masses m, and m, are situated in a system with ideal pulleys as shown in the figure. This system is in the vertical plane. A spring (constant k, rest length &) connects mass m: with the ground. Data: m= 1.5 kg, m2 = 2 kg, my= 1.5 kg, k = 50 N/m, & = 0.4 m, h= 2 m.

Two masses m, and m, are situated in a system with ideal pulleys as shown in the figure. This system is in the vertical plane. A spring (constant k, rest length &) connects mass m: with the ground. Data: m= 1.5 kg, m2 = 2 kg, my= 1.5 kg, k = 50 N/m, & = 0.4 m, h= 2 m.

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Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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