Simple Mass Spring System Homework: Finding Distance, Work, and Power

Other equations you could use include Hooke's Law (F=-kx), the equation for work (W=Fdcosθ), and the equation for power (P=W/Δt). In summary, the conversation discusses a mass-spring system mounted on a frictionless horizontal surface with a spring constant of 27 N/m and a block with a mass of 7 kg compressing the spring a distance of 0.15 m. The block slides on the surface until it reaches an equilibrium length, where a coefficient of kinetic friction of 0.55 applies. The questions revolve around the distance the block slides, the work done by the spring and friction, and the power dissipated by friction. Possible equations to use include conservation
  • #1
Harshmau5
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0

Homework Statement



consider a mass spring system mounted on a horizontal surface. The left end of the spring is rigidly mounted, and the spring constant is 27 N/m. A block with a mass of 7 kg is placed on the right side of the spring and compresses the spring a distance of .15 m. The region on the horizontal surface under the spring from the barrier on the left side to the equilibrium length of the spring is frictionless. The region of the horizontal surface to the right of the equilibrium length of the spring has a coefficient of kinetic friction equal to .55.
A. How far does the block slide before it stops?
B. How much work is done on the block by the spring? How much work is done on the block by friction?
C. What is the power dissipated by friction?

Homework Equations

The Attempt at a Solution

 
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  • #2
I'm thrown off because I don't have the velocity of the block as it starts from rest and is launched by the spring. Do I use conservation of energy?
 
  • #3
Harshmau5 said:
Do I use conservation of energy?
That's a good start.
 

1. How do I find the distance in a simple mass spring system?

In order to find the distance in a simple mass spring system, you will need to use the equation: Distance = Amplitude * sin(2πt / Period). The amplitude is the maximum displacement of the mass from its equilibrium position and the period is the time it takes for the mass to complete one full oscillation.

2. What is the formula for calculating work in a simple mass spring system?

The formula for calculating work in a simple mass spring system is: Work = 0.5 * k * (Amplitude)^2. K is the spring constant, which is a measure of the stiffness of the spring. The work done is equal to the potential energy stored in the spring.

3. How do I determine the power of a simple mass spring system?

To determine the power of a simple mass spring system, you will need to use the equation: Power = (2π / Period) * (Amplitude)^2 * k. The period is the time it takes for one full oscillation and k is the spring constant. Power is a measure of how quickly work is being done.

4. Can I use the same formula for distance, work, and power in any simple mass spring system?

Yes, the same formulas can be used for distance, work, and power in any simple mass spring system. However, the values for amplitude, period, and spring constant may vary depending on the specific system.

5. How does the mass of the object affect the distance, work, and power in a simple mass spring system?

The mass of the object does not directly affect the distance, work, and power in a simple mass spring system. These values are determined by the amplitude, period, and spring constant. However, the mass can indirectly affect these values by changing the amplitude and period of the system.

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