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**1. Homework Statement**

Two masses m and 3m are joined together by a compressed massless spring of constant k = 750 N/m. When spring is released it pushes masses apart and they slide on a horizontal tabletop as shown below. Mass 3m slides to the right and its track is frictionless. Mass m slides to the left and part of its track of length of .75 m has a friction where mu = .15. Compression of the spring is .25 m. For the mass 3m there is a ramp at the end of the tabletop. The ramp makes an angle of 20 degrees with the horizontal. Mass m is .5 kg. A length of the table is 2 m. Spring regains its initial length before mass m starts to slide with friction and mass 3m reaches the ramp. Using the data given above answer the followings:

1. calculate the potential energy of the spring.

2. Calculate the speed of the mass m before it starts to slide with friction.

3. Calculate speed of the mass 3m before it enters the ramp.

4. Calculate the work of the friction force for the mass m.

5. Calculate the speed of the mass m when it leaves the table.

6. Calculate the speed of the mass 3m when it leaves the ramp.

7. For the mass m find the time that is required to reach the floor (from the edge of the tabletop to the floor).

**2. Homework Equations and attempt at a solution**

for problem 1: PE =KE, where PE = potential energy and KE = kinetic energy formula two equals .5K delta X^2. this means PE = (750*.25^2)/2 = 23.44 J

for problem 2 I believe you use V = square root (2KE)/m = square root 2(23.44)/.5 = 9.68m/s

I believe problem 3 is solved the same way but that we change the mass so V = 5.59 m/s

problem 4 I believe would use 2 formulas W = fd and F(f) = mu* mg, where F(f) = force friction so it would be mu *mg *d = .552 J

problem 5 if I am not mistaken would use the equation V = (square root 2g delta h) = square root 2 *9.81 * .9 = 4.2

Problem 6 is where I'm a little hazy. Also I am not sure If I'm using the right equations. I have not done mechanics since November so if some one could check my work I would very much appreciate it. Also please excuse the English my teacher is Russian and I wrote the problem word for word.