Why is the Height of a Mass Launched by a Spring Dependent on its Mass?

In summary, the conversation discusses a problem in which two masses of different sizes are launched from a platform on a spring and the question is what height they will achieve. The conversation explains that the height reached is independent of mass but the launch speed is dependent on mass. Equating the formulas for kinetic and gravitational potential energy results in an expression that is independent of mass. However, this only applies when the masses are launched together. When launched separately, the launch speed and height will vary.
  • #1
syang9
61
0
this problem came up in my mcat physics prep book. two masses, one twice as massive as the other, are placed on a platform atop a spring. when they're launched, what height do they achieve?

i know they reach the same height, and from a previously archived thread on this board, i understand (somewhat) the reason.. the elastic potential energy is first transformed to kinetic energy, which is then transformed to gravitational potential energy. equating the formulas for those two energies results in an expression that is independent of mass.

what confuses me is that this seems to imply that the height of a mass launched by a spring is independent of mass altogether. this is clearly false.. could someone explain why?
 
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  • #2
also, why is it incorrect to simply equate the elastic potential energy to the gravitational potential energy? this yields an expression that is clearly dependent on mass.
 
  • #3
syang9 said:
the elastic potential energy is first transformed to kinetic energy, which is then transformed to gravitational potential energy. equating the formulas for those two energies results in an expression that is independent of mass.
For a given launch speed, the height reached is independent of mass (equate KE to GPE). But the launch speed depends on the mass (equate the spring PE to KE).

what confuses me is that this seems to imply that the height of a mass launched by a spring is independent of mass altogether. this is clearly false.. could someone explain why?
It doesn't imply that.

Can you state the exact problem?

syang9 said:
also, why is it incorrect to simply equate the elastic potential energy to the gravitational potential energy? this yields an expression that is clearly dependent on mass.
It's not incorrect at all.

Perhaps you are mixing up (1) Two masses launched together, with (2) Each mass launched separately?
 
  • #4
hi syang9 ! :smile:
syang9 said:
also, why is it incorrect to simply equate the elastic potential energy to the gravitational potential energy? this yields an expression that is clearly dependent on mass.

I'll just add this to what Doc Al :smile: has said:

you can equate them, but how would that tell you how much of the energy goes to one mass, and how much to the other? :wink:
 
  • #5
Doc Al said:
For a given launch speed, the height reached is independent of mass (equate KE to GPE). But the launch speed depends on the mass (equate the spring PE to KE).



so then, the reason that two masses launched together reach the same height is because the launch speed is determined by the total mass, right? after they are launched, they must reach the same height because they are traveling at the same speed.
 
  • #6
Right!
 

FAQ: Why is the Height of a Mass Launched by a Spring Dependent on its Mass?

What is the concept of "Two masses on a spring"?

The concept of "Two masses on a spring" refers to a physical system where two masses are attached to the ends of a spring and are able to oscillate back and forth. The spring acts as a restoring force, causing the masses to move towards each other when stretched and away from each other when compressed.

What is the equation that describes the motion of "Two masses on a spring"?

The equation that describes the motion of "Two masses on a spring" is known as the spring-mass system equation. It is given by F = -kx, where F is the restoring force, k is the spring constant, and x is the displacement from equilibrium. This equation can be used to calculate the acceleration, velocity, and position of the masses at any given time.

What factors affect the motion of "Two masses on a spring"?

The motion of "Two masses on a spring" is affected by several factors. These include the mass of the masses, the spring constant, the amplitude of the oscillation, and any external forces acting on the system. The initial conditions, such as the initial displacement and velocity, also play a role in determining the motion of the system.

How does energy conservation apply to "Two masses on a spring"?

In a "Two masses on a spring" system, energy is conserved as the masses oscillate back and forth. The total mechanical energy of the system, which includes the potential energy stored in the spring and the kinetic energy of the masses, remains constant. This means that as the potential energy decreases, the kinetic energy increases and vice versa, resulting in a continuous exchange of energy between the two forms.

What are some real-life applications of "Two masses on a spring"?

The concept of "Two masses on a spring" has many real-life applications. One example is in the design and construction of suspension bridges, where the cables and towers act as the spring and the cars or pedestrians act as the masses. This system allows the bridge to withstand the weight of heavy traffic and natural forces such as wind and earthquakes. Another example is in shock absorbers used in vehicles, where the spring-mass system helps to absorb and dissipate energy to provide a smoother ride.

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