A block with a mass of 0.8 kilograms is connected to a 100 N/m spring on a smooth floor. One end of the spring is connected to a wall. The block is pulled to the right 5 centimeters and then released. What is the total energy of the system?
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00:00Hi friends, every word you read, every knowledge you learn is a savings for your future.
00:10A block connected to a spring is on a smooth floor surface.
00:16Apparently one end of the spring is attached to the wall.
00:21The block is then pulled to the right, then released.
00:25Well, we are asked to calculate the total energy of the system.
00:30As usual, we will show a short animation.
00:37At first the system is in equilibrium.
00:41The block and the spring do not move at all.
00:46Not long after that, an external force pulls the block to the right.
00:51Because the block is attached to one end of the spring, the spring will stretch following the position of the block.
01:01After the external force is removed, the block will move left and right periodically.
01:07The block performs simple harmonic motion.
01:09How do we calculate the total energy of the system?
01:16Simple.
01:18Let's look at when the external force is still acting.
01:21As long as the external force is still touching the block, the block remains motionless, but the spring has displaced from its equilibrium position.
01:33The spring will try to pull the block to the left, but the force is still acting there.
01:38Because the block has not moved, the energy stored in the spring is exactly the same as the energy exerted by the external force to keep the block from moving.
01:49Mathematically, the external force is equal to the spring force.
01:53Let's say the spring displaces a distance A measured from its equilibrium position.
02:04The spring energy is half K A-squared.
02:09When the external force is removed from the system, the stored energy of the spring will be used to perform simple harmonic motion.
02:17In other words, the total energy of the system is nothing more than half K A-squared.
02:26Now let's look at some numbers listed on the problem sheet.
02:30The spring constant is 100 N per meter, and the maximum displacement of the block is 0.05 meters.
02:37I think this calculation is quite easy. The total energy is about 0.125 Joules.
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