00:01
This is a toy cannon marked in blue color and the red is the spring which is compressed by 4 .99 centimeter and the spring constant is 7 .95 newton per meter.
00:20
Ball mass is given 5 .27 gram.
00:25
So now spring is compressed so when spring is released the ball moves through the toy cannon.
00:33
In the barrel and the surface of the barrel exert a constant friction force of 0 .031 newton on the ball.
00:46
So we are supposed to find out the velocity with which the ball exits the cannon at point a, right? so this position is the compressed position of the spring.
01:03
We call it point b.
01:07
At point b, the total energy of the system is nothing but the potential energy of the spring, compressed spring.
01:18
So we know the potential and means energy of the compressed spring is one half kx square where x is the compression in the spring.
01:29
The value of x is 4 .99 centimeter and k is the spring constant.
01:34
And the spring constant is given as 7 .95 newton per meter.
01:40
With this energy, the ball starts to move.
01:43
So when the ball reaches to point a, exit point, it has its kinetic energy, 1 half mv square, and plus some work is done by this spring potential energy against the force of friction.
02:05
So the potential energy at point b is converted into the kinetic energy at point a plus the work done between the inside the barrel against the force of friction.
02:22
Now this work done is equal to force of friction multiplied by the distance.
02:30
Now here the distance is the distance the ball travels inside the barrel and the force of friction is given as 0 .031 newton per meter.
02:49
So we have all the data so we can just solve.
02:55
We want to find the velocity because we are interested to find the exit velocity.
03:02
So we can write 1 half mv square is equal to 1 half kx square minus force of friction multiplied by distance.
03:26
So if we solve this further, we will get v is equal to under root kx square minus 2 times force of friction into distance divided by the mass.
03:52
We have all the values.
03:54
We have value of k is given.
03:56
X is 4 .99 centimeter.
03:59
Force of friction is given.
04:00
Distance is 15 .2 centimeter.
04:03
Mass is also given.
04:05
So if we solve this, it comes out to be 1 .403 meter per second.
04:13
This is the exit velocity of the ball which is the answer for our first part right now this is the spring part the point a shows the position of the spring without any compression now we compress the spring inside the cannon by 4 .9 cm the spring reaches to point b right spring reaches to point b now from point b when spring again decompress and move towards point a during its motions from b to a the spring force acts in the right direction and tries to increase the velocity of the spring at the same time the force of friction acts in the opposite direction like the spring force acts in this direction while force of friction acts in the opposite direction.
05:36
Force of friction will try to reduce the velocity of the spring while the spring force will try to increase the velocity of the spring.
05:47
Now there will be a point because the force of spring force, kx, will work only between point b to point a.
06:00
After the point a, the spring will again return to its normal position and there will not be any spring force.
06:10
So between point b to point a, there will be a point where the spring force will be zero.
06:19
Because force of friction will reduce the spring force zero before point a...