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## Physics library

### Course: Physics library>Unit 5

Lesson 2: Springs and Hooke's law

# Spring potential energy example (mistake in math)

A spring, a frozen loop-d-loop and more! Explore the concept of energy conservation with a thrilling ice loop-d-loop scenario as you see how potential energy from a compressed spring can propel a block of ice through a loop, using kinetic and gravitational energy. (See if you can find the mistake I made and get the right answer!). Created by Sal Khan.

## Want to join the conversation?

• Can anyone explain to me what is the mistake in sal's calculations?
Is it taking potential energy as 10x^2 instead of 5x^2, or is it something else? •   You found the mistake! Sal's slip up didn't impact anything until the final answer. Instead of saying x^2=g, he should have said x^2=2g. Thus, you can multiply Sal's answer by √2 to get the real answer.
• I'm sorry but according to the diagrams it seems as if the cube would be upside down when it reaches the bottom side of the curved surface. Wouldn't that mean that the the downward force wouldn't just be the force of gravity but also the normal force? I do believe the only way to have only a downward gravitational force would be if the ice is on the top side of the curved surface, but the diagrams makes it seem otherwise the opposite. •  By definition, the normal force is the force perpendicular to the surface of the plane an object contacts. In other words, it is the force exerted by the surface of a plane that resists an object going through it (remember, Newton's law about equal opposite forces). (Think about your hand pressing into a table as you lean on it. If the normal force isn't enough to resist the force of your hand, your hand will go right through it.)

In most cases, when an object rests on top of a surface--such as a block on the ground--the normal force points upward while the gravitational force points downward. However, this isn't always the case (these forces do not always point completely opposite each other)--the definitions hold but the direction changes with the position of the object and surface of the plane it rests on. For example, when a block is on a inclined plane, the gravitational force is still downward (or toward the center of the earth) and the normal force is still perpendicular to the surface of the plane, but it is at angle (leaning away from the vertical axis the gravitational force is on) from its original position when it was resting on the ground.

So at the top of the loop de loop, the normal force is downward,but it only works to resist the ice block breaking the through the surface and leaving the loop (otherwise, the ice block might fly out of the loop), but not to push the block in a particular direction. Likely, because gravitational force is downward (or away from the surface of the icy loop), there may be little or no normal force at the top of the loop since there is no noticeable force pushing against the loop's surface. I believe this is why the normal force can be ignored in these calculations. Again, gravitational force is always toward the center of earth (that is, if your problem scenario is on the earth), which is still downward.

Hope this helps. :)
• If Sal didn't do the mistake, is "x" suppose to have come out to about 3.95m? • I got x to equal about 4.5m because I rounded g to 10m/s^2. The mistake is in the equation of PE. PE=1/2 K X^2. Since K is equal to 10 in the example he used, PE=(1/2) (10) x^2 which simplifies to PE=5X^2, If you continue this problem and solve for x..... 1/2mv^2 + mgh=5X^2 you should get about 4.5m. Sal forgot about the 1/2 and continued the problem with PE=10X^2 instead of 5X^2. Hope that helps :)
• doesnt the spring have kineic energy also when it is moving horizontally?
why only potential energy? • What does the value of spring constant " K" depend upon?
thank you • Why do we not use Normal force for centripetal force they both are in the same direction and also has magnitude(in this case 4x10=40 Newton)? • Can you please tell me that why the centripetal acceleration =9.8m/s^2 ? • I am still confused as to why the centripetal acceleration is the acceleration of gravity.
In the video, for the net force, he includes the force of gravity and the normal force which points towards the center and equaled it to v^2/r which is the centripetal acceleration • If the ball is going to just make it through the top of the loop, then that means the ball is right on the edge of losing contact with the track at the top. That means the track is not applying force to the ball. That means the only force available at that moment to provide the necessary centripetal acceleration at that moment is the weight of the ball. If the ball is going very fast then the track will also have to provide some of the necessary centripetal force at that moment; the weight of the ball won't be enough.
(1 vote)
• at , why did you chose that point ( the top of the loop de loop) to be the Efinal, why didn't you chose the bottom of the loop de loop??  