Find Initial Separation d for Mass-Spring System: Energy & Force | 4245 N/m

In summary, the conversation discusses a scenario where a mass slides down an incline and compresses a spring before coming to a stop. The goal is to find the initial distance between the mass and the spring. The speaker correctly uses the equations 1/2 kx^2 and mgh to find the potential energy and vertical distance, but must also use trigonometry to find the total distance along the incline.
  • #1
ViewtifulBeau
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A 21.4 kg mass starts from rest and slides a distance d down a frictionless 35.6 degree incline where it contacts an uncompressed spring of negligible mass, as shown. The mass slides an additional distance 0.2413 m as it is brought momentarily to rest by compressing the spring (force constant k = 4245 N/m). Find the initial separation d between the mass and the spring.

i used 1/2 kx^2 to find the PE of the block after being compressed to be 123.584 J. then i used mgh to find h. so 123.584/(35.6*21.4) = 1.011 m... but its not right. what did i do wrong? thanks.
 
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  • #2
You found the vertical distance h that is traversed, what they are asking for the the distance d along the incline it travels. You have the y-component of the distance, now you have to calculate the hypoteneuse which is d.

You did everything right, you just didn't take the final step.
 
  • #3
so i divided 1.011 by sin 35.6 but it is still not right. (1.7367)
 

Related to Find Initial Separation d for Mass-Spring System: Energy & Force | 4245 N/m

1. How do you determine the initial separation for a mass-spring system?

The initial separation, or equilibrium position, for a mass-spring system can be determined by using the equation d = F/k, where d is the initial separation, F is the force applied to the mass, and k is the spring constant. This equation is derived from Hooke's law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.

2. What is the significance of the spring constant in a mass-spring system?

The spring constant, denoted by k, is a measure of the stiffness of a spring. It determines how much force is required to extend or compress a spring by a certain distance. In a mass-spring system, the spring constant is a crucial factor in determining the initial separation and the amount of energy stored in the spring.

3. How does the energy of a mass-spring system vary with changes in the initial separation?

The energy of a mass-spring system is directly proportional to the square of the initial separation. This means that as the initial separation increases, the energy stored in the spring also increases. Conversely, decreasing the initial separation results in a decrease in the energy of the system.

4. What role does force play in a mass-spring system?

In a mass-spring system, the force is responsible for causing the spring to displace from its equilibrium position. The amount of force applied to the mass determines the initial separation and the amount of energy stored in the spring. As the mass moves away from the equilibrium position, the spring exerts a restoring force that brings the mass back to its initial separation.

5. How does the mass of an object affect the initial separation in a mass-spring system?

The mass of an object does not directly affect the initial separation in a mass-spring system. However, it does affect the force required to displace the spring from its equilibrium position and the amount of energy stored in the spring. The heavier the mass, the greater the force needed to cause displacement and the more energy stored in the spring at a given initial separation.

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