00:00Hi friends, if you are tired, take a break.
00:05Don't stop, let alone be lazy.
00:08Keep learning, keep growing.
00:11A stone is tied to a rope.
00:15When the rope is rotated vertically, the stone will reach various heights.
00:21Now we are asked to find the change in velocity of the stone between two different points.
00:30As usual, we will present a short animation.
00:35This vertical axis represents the height.
00:39The end of the rope is at the center of coordinates that the other end is connected to the stone.
00:47The stone performs a vertical circular motion.
00:51We see the speed of the stone at the lowest point.
00:55Just give an index of 1 to that point.
00:59Point 2 is the point when the rope is parallel to the horizontal axis.
01:04Actually, there are two possibilities.
01:08Let's just choose the point on the right as point 2 because point 2 must be reached after point 1.
01:15At these two points, the linear velocity of the stone is different.
01:19V2 is not equal to V1.
01:24How do we calculate the velocity at point 2?
01:28As long as there are no external forces and energy dissipation, the mechanical energy of the system is conserved.
01:35We can compare the mechanical energy at both points.
01:41Mechanical energy consists of kinetic energy and potential energy.
01:47We can cross out the mass of the stone.
01:53The height at the potential energy depends on the chosen reference.
01:58Since the axis of rotation is at the center of coordinates, the height of point 1 is the negative length of the rope and the height of point 2 is zero.
02:09From here we can get the velocity at point 2.
02:16But we have to know that velocity is a vector quantity.
02:21The directions of vectors V1 and V2 are different.
02:25They cannot be subtracted like subtracting two ordinary numbers.
02:31The difference of two vector quantities is also a vector quantity.
02:35The vector delta V is equal to vector V2 minus vector V1.
02:42Graphically, minus vector V1 is a vector whose direction is opposite to the direction of vector V1.
02:50Fortunately, the directions of the two velocities form a 90 degree angle.
02:55So the magnitude of vector V is the length of the hypotenuse of a right triangle.
03:02Delta V is equal to the square root of V1 plus V2 squared.
03:09We already know the vectors V1 and V2.
03:13This is the magnitude of delta V.
03:18Now we can see the magnitude of the velocity of V1 and the length of the rope.
03:24Delta V is equal to 2 root 2 meters per second.
03:29This is the magnitude of the change in velocity of the stone between point 1 and point 2.
03:36That is or the number will help you define this block.
03:37High-long- saving range praise!
03:38Happy learning everyone!
03:39Happy learning everyone!
03:40See you in the next video today!
03:41clin instruction with V2 dot.\
Comments