00:01
In question number one, the mass is equal to 2 kg and extension in the spring length x is equal to 4 cm which is 4 into 10 -2 meter.
00:26
We need to find out the spring potential energy.
00:31
First we will find out the spring constant.
00:34
Spring constant is equal to the force applied on the spring.
00:38
On the spring upon the displacement.
00:42
Now force applied is actually the weight.
00:45
Weight is pulling the spring downward.
00:48
So force is equal to weight.
00:50
Weight is mg upon x.
00:55
Now the spring potential energy we know it is one half kx square.
01:04
Now we put all the values.
01:07
K is mg upon x into x square it means it is one half m g x is the potential energy we have all the values mass is given as two pg g is 9 .8 meter per second square g and x is 4 into 10 x to minus 2 meter if we solve this it comes out to be 3 .92 into 10 -2 minus 1 june.
01:57
Now in part b, the mass of the wheelbarrow is m equal to 1 .5 kg.
02:11
It is initially at rest means initial velocity is zero.
02:17
And we apply a force of 4 .5 newton and under the action of this force it moves a distance of 0 .8 meter right so f and d are given we need to find out the kinetic energy and we know that kinetic energy is equal to one half mv square now to find the v we use equation of motion b square minus u square equal to 2 as u is zero it means v square is equal to 2a s or we can say v is equal to under root 2 as so right now what is the acceleration a a is equal to force upon mass force is 4 .5 newton mass is 1 .5 kg so acceleration is equal to 3 meter per second square we put this value acceleration here so velocity will become two acceleration is three meter per second square and distance travel is 0 .8 meter so it comes out to be 2 .19 meter per second is the velocity after it has traveled the distance of 0 .8 meter under the action of force 4 .5 newton now we put this value here so kinetic energy will become one half mass is 1 .5 kg and velocity is 2 .19 meters square.
04:18
It comes out to be 3 .59 jude.
04:27
Now, means another part of this problem, how much work is needed to stop the wheelbarrow.
04:39
Now we know the when the we know the work done is equal to change in the kinetic energy of the wheelbarrow because there is no change in the potential energy so change in kinetic energy means final kinetic energy minus initial kinetic energy so as the wheelbarrow stops so its final kinetic energy is zero minus initial kinetic energy we have calculated it is 3 .59 so work done is equal to minus 3 .59 now we'll come to the part c.
05:26
The car starts to fall from point o and it hits the ground at point d, i mean on the ground level, and the total distance it falls is 100 meters.
05:45
Now we have to find out its total energy, kinetic energy, potential energy and velocity after each 25 meter it falls.
05:54
It means we need to find out the value at point a when it falls first 25 meter, then we have to find out the value at point b when it falls another 25 meter, then value at point c it falls another 25 meter and value at point d where it falls 100 meters.
06:15
Now we start first point o, point o.
06:25
Now at point o, the potential energy is equal to m -g.
06:31
So, mass of the car is first we need to find out the mass of the car.
06:41
So let us first find out the mass of the car.
06:48
We know that at point o, the potential energy is equal to mgh is equal to 100 ,000 joule and this is equal to m is the mass of the car, g is the gravitational acceleration, and and height is 100 meter.
07:17
So this means the mass comes out to be 100 ,000 upon 9 .8 into 100 means 102 .04 kg.
07:39
Right? so this is the mass of the car.
07:42
M is equal to 102 .04 kg.
07:48
Now when car is at point a, its height above the means ground is 100 minus 25 meters because it has already fallen 25 meter so remaining height above the ground is 75 meter so its potential energy is equal to m gh and m is 102 .04 g is 9 .8 height is 75 so its potential energy is 7499 .4 june right now what will be its velocity when it has traveled 25 meters distance to find out the value means velocity we use equation of motion b square minus u square equal to 2 as because the car starts to fall from rest u is zero it means the velocity is to under root 2g h here a equal to g and s is equal to h is the vertical height it has fallen so at point a it has fallen 25 meter so velocity will be 2 into 9 .8 into 25 it will be 2 into 9 .8 into 25 right so velocity comes out to be 22 .13 meter per second and its kinetic energy kinetic energy will be equal to one half mb square so mass is given as 102 .04 and b square will be 22 .13 whole square right so the kinetic energy comes out to be two 24999 .8 jude and the total energy will be equal to potential energy plus kinetic energy and potential energy is 74999 .4 plus kinetic energy is 2499 .9 .8.
10:40
This comes out to be 5 .9 .9 .2 .5 .5.
10:46
2 jules.
10:51
Now at point b at point b its potential energy will be mass 102 .4m g is 9 .8 it is 102 .0 4 g is 0 4 g is 9 .8 and what is the height of the car at point d height is total height might the height it has already fallen, means 100 minus 50...