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Problem 20 Easy Difficulty

Block A in Fig. 8.35 has mass 1.00 $\mathrm{kg}$ , and block $B$ has mass 3.00 kg. The blocks are forced together, compressing a spring $S$ between them; then the system is released from rest on a level, frictionless surface. The spring, which has negligible mass, is not fastened to either block and drops to the surface after it has expanded. Block $B$ acquires a speed of 1.20 $\mathrm{m} / \mathrm{s}$ , (a) What is the final speed of block $A ?$ How much potential energy was stored in the compressed spring?

Answer

(a) $\overrightarrow{\mathrm{v}}_{A 2}=3.6 \mathrm{m} / \mathrm{s}$ to the left.
(b) $U_{e l, 1}=8.64 \mathrm{J}$

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Video Transcript

{'transcript': "We have given two blocks one ofthe Mass one kitty and another off Mass. Three kilograms. And these are on the two sides of a compress spring. Then the spring is late to expand I. It's singular. Ground flock starts moving with velocity of 1.2 zero meters per second. Let's say the one kilogram object most with their last week. No for party. We need to find the velocity for that. They simply need to apply conservation of momentum. Because when the spring was just released, what off the objects had zero velocity? The initial mourned him. We'll see. Which means the final moment. I'm also has to be zero because there are no other external forces in the horizontal direction. Ofcourse, that is forced to it in the spring. But that's an internal force for this system. And the only external force Wait is what now? The final moment amounted to walk off the system. Is the momentum off system eh? Let's call the 1st 1 a project. And the 2nd 1 object and they went off to be. Now we know that Ivan Wyndham, off object, we simply mass multiplied by the velocity, which is three times 1.2 and for object A. The momentum is one multiply where they were lost to me. But not that our velocity is in the opposite direction. And hence we need a minus sign here. Now this is equal to zero, which gives us the velocities three times, one point to just 3.6 meter per second. Now that we found this or party, we want to find out the amount of energy in the compass spring. Now, because of conservation of energy, the kind of unity off these two blocks must be equal to the amount of energy expert used by the by the spring, which is the amount of energy in the spring. So the amount of energy stored in the spring is equal to the sums off the kinetic energies, which is the kind of energy off object in Let's the conductivity ofthe abjectly of the kind of energy off object is simply happens mass, which is one kilogram multiply by. We'll ask a square, which is 3.6 square. Let's for object, be half thanks. Mass is three kilograms on the velocity is 1.2 and then squared. Excuse us a Pontiac for Jules"}