A slingshot will shoot a 10-g pebble 22.0 m straight up. (a) How much potential energy is stored in the slingshot's rubber band?

Video transcript

Hey everybody. So today we're dealing with some problems about the conservation of energy and specifically gravitational potential energy. So we're being told that we have a five g ping pong ball that is fired straight up in the air using the elastic energy that has been stored in a rubber band of a slingshot At a height of 10 m above the release point. The speed of the ball is zero. With this, we're being asked to calculate how much potential energy is stored in the band. So let us just conceptualize this real quick. We have a slingshot. This is a very crude slingshot. But let's just say this is our slingshot And we have a ball a ping pong that is five g. There's a massive 5g mass is equal to five g and it is launched into the air. It is launched. So at a height of 10 m, let's just say that is 10 m. So at 10 m, the change in height At 10 m at this point V. is equal to zero. The speed of the ball is 0m/s. So with this in mind. And with all this information, let's go ahead and start sort of solving So we know to the conservation of our the law of conservation of energy that K. One the kinetic energy of the first system plus the potential energy will equal d kinetic energy of the second plus the potential energy of the second, essentially telling us that the total energy here will not change, It'll be constant throughout. So we know that at the initial and the final position, the positions that we're concerned about kinetic energy will be zero due to the fact that the velocity of the ball is zero. So we know that you one must be equal to you too. With this, we can therefore decide that the change in potential energy will simply be U two minus. You want an easier way to think about this. Still would be considering the gravitational potential energy. Recall that gravitation potential energy is equal to the mass of the object, multiplied by the our acceleration due to gravity multiplied by the change in height. So the change in potential energy will also be the change in gravitational potential energy. Be the change in gravitational potential energy. Well that is right. Then change in your gravitational potential energy which is equal to uh five g. And we're going to multiply this by a conversion factor because we need to be working with S. I. Units. So we can recall That for every one kg We have 10 to the third or 1000 crams. Programs will cancel out the acceleration due to gravity is 9.8 m per second squared 9.81 m per second squared. And the change in height because it only goes 10 m high. And then if the speed of the ball is there, that means that's all to the point where the ball, the ping pong ball starts its descent Then the height, Delta Y. is 10 m Simplifying this, we get a final answer Of 0.49 jewels. Therefore The potential energy contained in the rubber band is 0.49 jewels, or answer choice B. I hope this helps, and I look forward to seeing you all in the next one.