00:00Hi friends, welcome to those of you who have just found this channel.
00:08This channel is one of the channels that provides educational materials in the form of animations.
00:17This is the question that we will discuss in this series.
00:21The question is quite long.
00:23You can read this question for 10 seconds.
00:38Do you understand this question correctly?
00:42Let's watch the following short animation.
00:46There are two stacked blocks connected by a rope.
00:50The rope connecting the two blocks is passed to a pulley.
00:54Thus, when the rope moves, the movement of the rope can rotate the pulley.
01:04Then the block at the bottom is pulled to the right by an external force.
01:09Of course the block pulls the rope behind it.
01:14The pull of the rope then pulls the block above the block.
01:20So the two blocks move in opposite directions.
01:23If the lower block shifts to the right, the upper block will move to the left.
01:31Now we are asked to draw the force lines acting on this system.
01:37Of course the equation of motion of the block.
01:41And the last is the magnitude of the external force needed for the system to move at a constant
01:46speed.
01:50Now we understand.
01:54Let's start answering the first part of this question.
02:00Before going further, we will identify some important quantities.
02:06Let's say the mass of the upper block is m1.
02:09The mass of the lower block is m2.
02:14The surface of the block and the floor are not slippery.
02:17There is a coefficient of static friction.
02:23The magnitude of the coefficient of static friction between the surface of the block
02:27and the floor and between the surface of the block and the block is the same, namely mu.
02:34For the pulley, there is no information in the question.
02:38We can ignore the movement of the pulley.
02:44An object moves or does not move because it is influenced by the force acting on the object.
02:51For the upper block, this block gets a gravitational force of m1g downwards.
02:58This block does not penetrate the surface of the block below it.
03:02Of course, block 1 gets a normal force and 1 upwards.
03:08This block is connected to a rope.
03:10There is a rope tension force.
03:12The direction is in line with the rope.
03:17Because both surfaces of the block are rough, the upper block will get a static friction
03:21force to the right, Fk1.
03:25It seems that this is the only force diagram for block 1.
03:31For the lower block, we do not know the magnitude of the external force.
03:35The force is F.
03:40Block 2 is also connected to the rope.
03:42There is also a rope tension force.
03:47For the surface of the block and the surface of the floor, there is a friction force Fk2
03:52to the left.
03:55The magnitude of the gravitational force acting on the lower block is m2g.
04:03Is this the only force acting on block 2?
04:06Let's look again more carefully.
04:10The force is an external action.
04:14Where there is action, there is reaction.
04:17This is true, isn't it?
04:21If at the top a force Fk1 works to the right, of course a force of the same magnitude and
04:26opposite direction will also work on block 2.
04:31This means that block 2 also works force Fk1, but the direction is opposite to the
04:36direction of Fk1 on block 1.
04:40You can understand this, if you have time to watch the motion dynamics course on this
04:45channel.
04:47Furthermore, the upper block presses on the lower block.
04:52Thus, the molecules in the lower block push the upper block with a force known as the
04:57normal force, N1.
05:01This force N1 arises due to the pressure from the upper block.
05:07This means that the lower block also has a force N1, but its direction is opposite to
05:12the force N1 acting on block M1.
05:18One more thing, the lower block presses on the floor surface.
05:22Of course the floor surface will provide a reaction force that is directed upwards.
05:27This force is none other than the normal force N2, which is directed upwards.
05:34So on the lower block there are two normal forces working at once.
05:41This is the force diagram in this system.
05:47Now we will answer the second part.
05:51Newton's laws work for every object.
05:54Different objects apply different Newton's laws.
06:00For the first block, we will write the equation in two directions, the vertical direction
06:04and the horizontal direction.
06:08For the vertical direction, the block does not move up or down.
06:14The resultant force in this direction is zero, and 1-M1g is equal to zero.
06:23For the horizontal direction, the block moves to the left.
06:26So the direction to the left is positive.
06:30In motion analysis, the direction that is in the same direction as the direction of
06:34motion has a positive sign.
06:37T-fk1 is equal to M1a.
06:41Since the question has mentioned that this system is moving at a constant speed, the
06:46acceleration value is zero.
06:51For block 2, we will also analyze the resultant force in two directions.
06:57For the vertical direction, there are three units of force.
07:00N2-N1-N2g is equal to zero.
07:07For the horizontal direction, block 2 moves to the right.
07:16F-fk1-fk2-t is equal to zero.
07:21The resultant force is zero, because this system is moving at a constant speed.
07:29These are the four equations of motion for objects M1 and M2.
07:34Knowing these four equations, we can calculate the magnitude of the external force.
07:42We start from the equation that looks the simplest.
07:47Let's write, from equation 1, N1 is equal to M1g.
07:54Next is this equation.
07:59T is equal to fk1.
08:04The friction force is mu multiplied by the normal force.
08:10T is equal to mu M1g.
08:15Now is this equation.
08:19N2 is equal to N1 plus M2g.
08:25We already know the value of N1.
08:30N2 is equal to M1 plus M2, multiplied by g.
08:37Next is this equation.
08:42F is equal to fk1 plus fk2 plus t.
08:48All of these values are also known.
08:53F is equal to mu times 3M1 plus M2, g.
09:00This is the external force required to pull the block so that the system moves at constant velocity.
09:09Hope this helps.
09:11Don't forget to watch the next video.
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