Laws of Motion -08- Acceleration of Blocks Pushed by External Force

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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.

Transcript

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!

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