There is three parts In the figure below, block 2 of mass 2.0 kg oscillates on t

Question

There is three parts In the figure below, block 2 of mass 2.0 kg oscillates on the end of a spring in SHM with a period of 20 ms. The block's position is given by x - (1.0 cm) cos(omegat + pi2). Block 1 of mass 4.0 kg slides toward block 2 with a velocity of magnitude 6.0 m/s, directed along the spring's length. The two blocks undergo a completely inelastic collision at time t - 5.0 ms. (The duration of the collision is much less than the period of motion.) a) Find the spring's spring constant. b) Find the velocity of the blocks after collision. c) What is the amplitude of the SHM after the collision? The Recorder must list all the members of the group. with the writers name first, on the paper submitted You may ask the TA questions. the TA will provide answers that will help you get to the solution in the form of suggestions or other questions You mav not consult am books or notes. You should discuss the question quietly with other group members. The solution should be written out in the following form: Statement of the problem as given What needs to be found and how you think you will find it. Draw any diagrams that you need, more can be added later State any equations or relationships you think are relevant and say what each variable is. and if it has value, what its value is. You then procecd to solve the problem introducing new diagrams, equations. Statements of

Explanation / Answer

Given that;

m1 = 4.0 kg;

m2 = 2.0kg;

T = 20 ms;

v1 = 6m/s;

Part A:

The spring constant, k = 42 m1 / T2 = [4 * 3.14 * 3.14 * 4] / (20 x 10-3)2

k = 1.97 x 105 N/m

At collision, t = 2t / T = / 2

so that;

x = -x m;

If the spring is stretched at this moment is 1 cm we have x m = - 0.01m;

Part B:

From conservation of momentum we have,

m1v1 = [m1+m2] v

v = 4 * 6 / 6

v = 4 m/s

Speed of the blocks in common after collision is v = 4 m/s

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