Spring Ramp Problem: Maximum Distance for Compressed Spring Calculation

In summary, a 500-g block is released from rest and slides down a frictionless track, hitting a horizontal surface at the bottom where it sticks to a light spring with a constant of 20 N/m. Using the equation mgh=1/2kx^2, the maximum distance the spring is compressed is found to be 0.99 m.
  • #1
BBallman_08
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Homework Statement



A 500-g block is released from rest and slides down a frictionless track that begins 2.00 m above the horizontal as shown in the figure. At the bottom of the track, where the surface is horizontal, the block strikes and sticks to a light spring with a constant of 20 N/m.find the maximum distance the spring is compressed.

Homework Equations



I am pretty sure that this is just an MGH type problem, so I used :

mgh=1/2kx^2



The Attempt at a Solution



Using the above formula, I calculated: (.500)(9.8)(2)=.5(20)(x^2)

Solving the equation for value x i get .99 m.

Can anyone advise me to whether this is correct or not?
 
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  • #2
That is correct.
 
  • #3
awesome, thanks alot!
 

1. What is the purpose of the spring/ramp problem?

The spring/ramp problem is a common physics problem used to demonstrate the relationship between energy, force, and motion. It involves a mass attached to a spring on a ramp and is used to understand the concepts of potential and kinetic energy, as well as the effects of gravity and friction on an object's motion.

2. How is the spring/ramp problem set up?

The spring/ramp problem typically involves a ramp, a spring, a mass, and some type of measuring device to record the motion of the mass. The mass is attached to the spring and placed on the ramp, and the ramp is tilted at a certain angle. The motion of the mass as it moves up and down the ramp is then observed and recorded.

3. What factors affect the motion of the mass in the spring/ramp problem?

The motion of the mass in the spring/ramp problem is affected by several factors, including the mass of the object, the spring constant of the spring, the angle of the ramp, and the presence of any external forces such as friction. These factors can be altered to see how they affect the motion of the mass and to better understand the principles of energy and motion.

4. How is energy conserved in the spring/ramp problem?

In the spring/ramp problem, energy is conserved as the mass moves up and down the ramp. When the mass is at the top of the ramp, it has potential energy, which is converted into kinetic energy as it moves down the ramp. As the mass moves back up the ramp, it loses kinetic energy and gains potential energy again, and the cycle continues. This demonstrates the principle of conservation of energy.

5. What real-life applications can be modeled using the spring/ramp problem?

The spring/ramp problem has many real-life applications, such as understanding the motion of a car going over a hill or the motion of a roller coaster. It can also be used to study the motion of objects on an incline, such as a ball rolling down a hill. By understanding the principles of energy and motion in the spring/ramp problem, scientists can better understand and predict the behavior of objects in the real world.

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