How much is the spring compressed by in the following case: A 2 kg disk falls from a height of 20 m and lands on a compressible spring with a spring constant of 10 N/m.
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
When the disk falls from a height on a spring, the potential energy that was stored in the disk due to its being at a height is converted to potential energy stored in the spring due to it being in a state of compression.
The total energy in the system remains the same (assuming there is no loss due to heat etc.), only the form of the energy changes.
Let us consider the information that is provided. The mass of the disk is 2 kg, its height is 20 m and the spring constant of the spring in 10 N/m.
The potential energy stored in the spring is equal to m*g*h
= 2*9.8*20
= 392
Now assume the disk falls a complete distance of 20 m and the spring is compressed by x m.
The energy stored in the spring is given by (1/2)*k*x^2
So we have (1/2)*k*x^2 = 392
=> (1/2)*10*x^2 = 392
=> x^2 = 392*2/10
=> x = sqrt (78.4)
=> x = 8.85 m
Therefore the spring is compressed by 8.85 m.
Related Questions
- A mass of 10 kg is dropped on a spring 1 m long kept on the ground from a height of 5 m. If the...
- 1 Educator Answer
- What should the compression of the spring be so that the velocity of the ball when it is released...
- 1 Educator Answer
- When two springs with spring constants 4 N/m and 6 N/m in series are compressed by 2 m, by how...
- 1 Educator Answer
- An elevator is accelerating upward at 3.0 m/s^2. A 60kg student is standing stop a spring in the...
- 1 Educator Answer
- Two balls, each with a mass of 0.813 kg, exert a gravitational force of 8.38 x 10^-11 N on each...
- 1 Educator Answer
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.