Dropping a mass on a slope, entering a loop and stopping.

In summary, the teacher discussed a problem for an upcoming test where a mass is dropped on a slope that leads into a loop. The goal is to calculate the required height of the slope for the mass to complete one full loop. The slope is frictionless and the loop has a friction coefficient of μk=0.2. The problem involves using the work-energy theorem and considering the forces acting on the mass, including centripetal forces and the normal force at the top of the loop. Calculations can be done without using calculus.
  • #1
Jairo Rodriguez
1
0
Hello, today our teacher told us that on tomorrow's test there is going to be a problem where you drop a mass on a slope which connects into a loop. The point of the problem is to calculate exactly how tall the slope must be for the mass to complete exactly one course through the loop.

CoasterH%3D2.5r.gif

(https://upload.wikimedia.org/wikipedia/commons/1/10/CoasterH%3D2.5r.gif, I think it looks better from there.)
I hope this helps to visualize. The idea is that I drop the object on h height, and then it travels down the slope which is frictionless, then enters the loop which has friction, μk=0,2. I have to express algebraically the height required for the mass to stop after it has completed exactly 1 turn. The turn starts when the mass "starts going up" the loop.

I have tried doing this, I even asked another teacher (an assistant) how to do it, and he was unable to. I initially started with the usual stuff, U1 = K2, U1 at the start of the slope, K2 when the loop starts. Then I started calculating the K3 + U3 on the topmost part of the loop, but then I realized I have to take into account centripetal forces, also the normal force which it's different for every point on the loop, so I think I have to dive into calculus. I haven't done any calculus in my life, but if that's the only way to the answer, I am willing to do the necessary reading to at least understand the explanation.

That's all the info we get. If the post is badly redacted, I am sorry, spanish is my first language. If I wasn't clear on some point, let me know, I will try to fix it or explain myself as soon as possible. First time on this forum. Sorry again.
Thanks.
 
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  • #2
Jairo Rodriguez said:
I have tried doing this, I even asked another teacher (an assistant) how to do it, and he was unable to. I initially started with the usual stuff, U1 = K2, U1 at the start of the slope, K2 when the loop starts.
First of, use the work - energy theorem, not ΔU = ΔK - this is only defined for conservative forces.
Second, see which forces act on the body. Next, which of them do work. You also want to make the normal at the top just zero.No calculus will be involved in your calculations.

Hope this helps.
 

FAQ: Dropping a mass on a slope, entering a loop and stopping.

1. How does the mass's initial velocity affect its movement on the slope?

The mass's initial velocity plays a crucial role in its movement on the slope. If the mass has a high initial velocity, it will have more energy and will be able to travel further on the slope before coming to a stop. On the other hand, a lower initial velocity will result in the mass stopping at a shorter distance on the slope.

2. What factors contribute to the mass successfully entering a loop on the slope?

There are several factors that contribute to the mass successfully entering a loop on the slope. These include the mass's velocity, the angle of the slope, and the size of the loop. The mass must have enough velocity to overcome the force of gravity and maintain its circular motion within the loop.

3. How does the slope's angle affect the mass's movement?

The slope's angle has a significant impact on the mass's movement. A steeper slope will result in the mass moving faster due to the force of gravity, while a shallower slope will result in slower movement. The angle also affects the mass's ability to enter a loop, as a steeper slope may make it more difficult for the mass to maintain circular motion.

4. What role does friction play in the mass's movement on the slope?

Friction plays a crucial role in the mass's movement on the slope. It is the force that opposes the motion of the mass and can slow it down or even bring it to a stop. The amount of friction present will depend on the surface of the slope and the mass's weight. A smooth surface will result in less friction and a longer distance traveled by the mass.

5. How does the mass come to a stop on the slope?

The mass comes to a stop on the slope due to a combination of factors. These include the force of gravity, the slope's angle, and the presence of friction. As the mass moves along the slope, the force of gravity pulls it downwards, while friction and the slope's angle work against it. Eventually, these forces will cause the mass to slow down and come to a stop.

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