Explore the Motion of a Mass Along 3 Tracks

In summary, the problem involves three tracks, P1, P2, and P3, where P1 is similar to an "up-facing parabola," P2 is straight, and P3 is similar to a "down-facing parabola." A mass m is projected with the same initial horizontal velocity along each track, allowing it to reach the end at point B. The total travel times between point A and B for P1, P2, and P3 are t1, t2, and t3 respectively. The intuition is that t2<t1=t3.
  • #1
jan2905
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You will have to use your imagination: 3 tracks are constructed as such... path 1 (P1) is similar to a "down-facing parabola," path 2 (P2) is straight, and path 3 (P3) is similar to an "up-facing parabola." P1 is "uphill," P2 is "through that hill," and P3 "under the hill, beneath P2, and exactly 'oposite' of P1."

Okay! ... A mass m starting at point A (foot of the hill) is projected with the same initial horizontal velocity v along each of the three tracks (negligible friction) sufficient in each case to allow the mass to reach the end of the track at point B (oposite foot of the hill). The masses remain in contact with the tracks throughout their motions. The displacement A-B is the same in each case, and the total path length of P1 and P3 are the equal. If t1, t2, and t3 are the total travel times between A and B for P1, P2, and P3 respetively, what is the relation among these times?



I said intuitively that: t2<t1=t3. correct?
 
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  • #2
jan2905 said:
Okay! ... A mass m starting at point A (foot of the hill) is projected with the same initial horizontal velocity v along each of the three tracks (negligible friction) sufficient in each case to allow the mass to reach the end of the track at point B (opposite foot of the hill).
I said intuitively that: t2<t1=t3. correct?

What a nice little problem! Keeping in mind that the initial velocity is horizontal... Consider parabola (1) Will a horizontal velocity enable the mass to slide up over the hill? (If so, will it for ALL parabolas?) Consider parabola (2) The horizontal velocity will enable the mass to slide down the track. With no friction, what does conservation of energy tell you about the velocity of the mass when it reached point B? Finally, what is the relationship between the lengths of the straight line track and the parabolic track.

(As you may deduce from my comments, I have some qualms about the formulation of the problem, but it's still a nice problem. Substitute a cycloid for the parabola and tweak it a little and you have a classic physics problem...)
 
  • #3


Yes, that is correct. Since the mass is projected with the same initial horizontal velocity, it will take the same amount of time to travel through the straight path (P2) and the path with an equal total path length (P3). However, since P1 is uphill, it will take longer for the mass to reach the end of the track at point B. Therefore, t1 and t3 will be equal, but t2 will be smaller since it is a straight path with no incline. So, the relation among the times is t2 < t1 = t3.
 

Related to Explore the Motion of a Mass Along 3 Tracks

What is "Explore the Motion of a Mass Along 3 Tracks"?

"Explore the Motion of a Mass Along 3 Tracks" is a scientific experiment or activity that involves studying the movement of an object (mass) along three different tracks or paths. It helps to understand the concepts of motion, speed, velocity, and acceleration.

What materials are needed for this experiment?

The materials needed for this experiment include: a mass (such as a toy car or ball), three tracks (such as a ramp, a loop, and a straight track), a stopwatch or timer, a ruler, and a pen or pencil for recording data.

How do I set up the experiment?

Start by setting up the three tracks side by side on a flat surface. Place the mass at the starting point of the first track. Use the ruler to measure the distance between the starting point and the end point of each track. Use the stopwatch to time how long it takes for the mass to reach the end point of each track.

What are the variables in this experiment?

The independent variable in this experiment is the track that the mass travels on. The dependent variable is the time it takes for the mass to travel the length of the track. Other variables that should be kept constant include the mass of the object, the starting point, and the surface the tracks are placed on.

What can I learn from this experiment?

This experiment allows you to explore the relationship between distance, time, and speed. By measuring the time it takes for the mass to travel each track, you can calculate its speed and compare it to the other tracks. You can also observe how different tracks affect the motion of the mass, such as changes in velocity and acceleration.

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