I think the normal force becomes zero when the toy loses contact. But when I use this and calculate the angle you specified, and then calculate the height h coresponding to this angle, I get the non sensical anwser of h = -1 / 3 R, which seems really strange. Maybe I made a mistake that I didn't notice, but I still don't know why I can't get the right answer.Delta2 said:The key to this problem is to "translate" the statement "It loses contact with the track" to a fairly simple equation. In order to be of more accurate help I will ask you "Which of the forces on the toy becomes zero when it loses contact with the track". Set this force to zero so you have one additional equation together with the equations of conservation of energy and the equations of centripetal force.
Also I find it easier instead of the height to calculate the angle that the radius to the point of lost of contact makes with the horizontal.
Witdouck K said:I think the normal force becomes zero when the toy loses contact. But when I use this and calculate the angle you specified, and then calculate the height h coresponding to this angle, I get the non sensical anwser of h = -1 / 3 R, which seems really strange. Maybe I made a mistake that I didn't notice, but I still don't know why I can't get the right answer.
Yes that's right the normal force becomes zero. You got to write a detailed post giving all the details of what equations you made and how you worked with them and also a diagram with the track and the forces at the point of lost contact will be nice so I can pinpoint where you might have gone wrong.Witdouck K said:I think the normal force becomes zero when the toy loses contact. But when I use this and calculate the angle you specified, and then calculate the height h coresponding to this angle, I get the non sensical anwser of h = -1 / 3 R, which seems really strange. Maybe I made a mistake that I didn't notice, but I still don't know why I can't get the right answer.
On closer inspection, I indeed put the zeroth level of the potential energy at the starting point, I just didn't really realise it untill you pointed it out. When putting it at the center of the loop, I als got ##\frac{2}{3}R##, but I know this is just the same answer as ##\frac{-1}{3} R## because of the translation of the origin. Thanks a lot!Delta2 said:Yes that's right the normal force becomes zero. You got to write a detailed post giving all the details of what equations you made and how you worked with them and also a diagram with the track and the forces at the point of lost contact will be nice so I can pinpoint where you might have gone wrong.
If you cant type in Latex and make a diagram with some drawing software, I guess as a last resort you can post screenshots of your handwritten work of the problem.
By the way the answer I get for the angle is ##\sin\theta=\frac{2}{3}## . So the height is ##\frac{2}{3}R##. Come to think of it your height of -1/3R means that you might took as zero level of potential energy the level at the starting point. I took as zero level of potential energy the horizontal diameter of the loop.
P.S Actually no, its not where you put the zeroth level of potential energy but where you put your coordinate system. I put it centered at the center of the loop, it seems to me you put it centered at the starting point of the toy.
I think its not where you put the zeroth of PE but where you put the origin of coordinate system. Usually these two coincide, i.e the zeroth level of PE is the x-axis of the coordinate system but its not always the case.Witdouck K said:On closer inspection, I indeed put the zeroth level of the potential energy at the starting point, I just didn't really realise it untill you pointed it out. When putting it at the center of the loop, I als got ##\frac{2}{3}R##, but I know this is just the same answer as ##\frac{-1}{3} R## because of the translation of the origin. Thanks a lot!
To ensure the toy car completes the loop successfully, you need to adjust the height of the loop, the initial velocity of the car, and the radius of the loop. These factors must be carefully balanced to achieve the desired result.
Centripetal force is the force that acts on an object moving in a circular path, directing it towards the center of the circle. In the case of the toy car loop puzzle, centripetal force is essential for keeping the car on the track and preventing it from flying off the loop.
The angle of the loop affects the toy car's motion by influencing the amount of gravitational potential energy that is converted into kinetic energy as the car moves down the loop. A steeper angle will result in a faster car speed, while a shallower angle may cause the car to lose momentum and fail to complete the loop.
If the toy car does not have enough speed to complete the loop, it will lose momentum and fall off the track before reaching the top of the loop. Increasing the initial velocity of the car or adjusting the height and radius of the loop may help solve this issue.
To calculate the minimum speed required for the toy car to complete the loop, you can use the principle of conservation of energy. By equating the gravitational potential energy at the top of the loop to the kinetic energy at the bottom, you can determine the minimum speed needed for the car to successfully navigate the loop.