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# Spring potential energy example (mistake in math)

A spring, a frozen loop-d-loop and more! (See if you can find the mistake I made and get the right answer!). Created by Sal Khan.

## Want to join the conversation?

• Please explain why the centripetal acceleration at the top of the loop is equal to 9.8 m/s/s. •   9.8 m/s^2 is the value of acceleration due to gravity for objects near the Earth's surface.

Short explanation: the only inward force contributing to the centripetal acceleration at the top of the loop is the gravitational force.

Long explanation: Centripetal acceleration is the acceleration that causes an object to move in a circle. It is always an acceleration towards the center of the circle. Sal set the centripetal acceleration at the top of the loop equal to the acceleration due to gravity in order to find the minimum amount of initial potential energy needed for the block to move around the loop. The minimum amount of energy it needs would coincide with the block experiencing no inward force from the wall of the loop at the top, therefore making the only inward force the force of gravity.
• 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 :)
• from my understanding the centripetal acceleration/force isn't a real acceleration/force right? So at the top it's caused by gravity, but at a quarter into the loop, what causes it to move towards the left(center)? Also, I think your apparent weight can change if you're on top of the loop vs bottom of the loop, but i'm not sure why, can someone also further explain on this? • What does the value of spring constant " K" depend upon?
thank you • doesnt the spring have kineic energy also when it is moving horizontally?
why only potential energy? • 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? • 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 ?  