Two blocks of masses 2 kg and 5 kg are placed side by side on a smooth horizontal surface as shown in the figure. A horizontal force of 35 N is applied to the 2 kg block. Find:
(a) the acceleration of each block.
(b) the normal reaction between the two blocks.
(a) the acceleration of each block.
(b) the normal reaction between the two blocks.
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LearningTranscript
00:00Hey guys, Sunday is the perfect day to refuel your soul and be grateful for every blessing.
00:09Maybe this question is enough to recharge your mechanic skills after having fun on Sunday.
00:16We are asked to calculate the acceleration of the system and the normal force acting
00:20between two blocks pushed by an external force.
00:26Before going further, let's see this short animation.
00:31Two blocks adjacent to each other are on a smooth floor.
00:37An external force pushes one of the blocks from the left side.
00:41Both blocks move together to the right.
00:45As long as the external force pushes the blocks, the acceleration of the blocks will increase.
00:50Let's calculate the value of that acceleration.
00:55This system consists of two blocks.
00:59Each block is a separate body.
01:02So we have to draw a free body diagram for each block.
01:08For identification, let's call them block 1 and block 2.
01:15When block 1 moves to the right, the surface of block 1 will push the surface of block
01:192, causing the molecules on the surface of block 2 to be pushed to the right.
01:24This kind of pushing force is known as the normal force.
01:29In other words, the normal force acts on block 2 to the right.
01:35To return to its original condition, the molecules of block 2 will exert a force on block 1 to
01:40the left that is the same in magnitude but opposite in direction.
01:44This is the reaction force.
01:47Force N also acts on block 1 to the left.
01:52In addition to this force, there are also two other forces in the vertical direction.
01:57Gravitational force and the normal force to the floor surface.
02:02This is the force-free diagram of each body.
02:07Both blocks are accelerating to the right, meaning the direction of the acceleration
02:11is to the right.
02:15Force and acceleration are connected by Newton's law.
02:20In block 1, F minus N is equal to m1a.
02:26In block 2, N is equal to m2a.
02:31This is correct.
02:35We do not consider the force in the vertical direction because there is no frictional force
02:39and the block does not move in that direction.
02:44We have two equations with two unknown quantities.
02:48I think we don't need to find another equation.
02:54Just add the two equations.
02:57F is equal to m1 plus m2 times the acceleration.
03:04From here, N is equal to F divided by m1 plus m2.
03:11We can see the magnitude of the external force and the mass of the block from the problem
03:15sheet.
03:18This is an easy calculation at equals 5 meters per second squared.
03:26For the normal force, we can choose one of two equations.
03:32N equals 5 times 5.
03:36The result is 25 Newtons.
03:40This is the answer to this question.
03:45Happy learning everyone!