00:01
For this problem on the topic of conservation of energy, we are told that a 2 kilogram box is on a frictionless incline plane of 40 degrees.
00:08
It is connected by a cord that runs over a pulley to a spring, which has a spring constant of 120 newtons per meter, as we can see in the figure.
00:17
The box is released from rest whilst the spring is unstretched.
00:21
We want to find the speed of the box after it has moved 10 centimetres down the incline.
00:25
We want to know how far it is down the incline when it momentarily starts.
00:30
And we want to know the magnitude and direction of the box's acceleration at the instant that it momentarily stops.
00:37
Now we'll take the original height of the box to be y is equal to 0 as the reference level for gravitational potential energy and in general the height of the box y is equal to minus d sine 40 degrees.
00:54
And so using this in the conservation of energy, we have the initial kinetic energy, plus the initial gravitational potential energy at its topmost point is equal to its kinetic plus potential energy after it has moved down 10 centimeters.
01:11
So initially the gravitational potential, elastic potential and kinetic energy is all zero.
01:17
And finally, it has kinetic energy a half mv squared plus gravitational potential energy m, g, y, plus elastic potential energy a half k, d.
01:32
D squared...
