Solve Hooke's Law Problem: Spring Constant & Compression

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SUMMARY

The discussion centers on calculating the effective spring constant of a spring system in a taptap vehicle using Hooke's Law. Initially, the user calculated the spring constant as 2.94 x 10^4 N/m based on a 60 kg driver and a spring compression of 0.02 m. However, after loading the taptap with 25 passengers, three goats, five chickens, and bananas, the user miscalculated the spring compression, arriving at 1.80 x 10^4 N instead of the correct value of 0.5328 m. The key takeaway is the importance of accurately determining the total mass affecting the spring system.

PREREQUISITES
  • Understanding of Hooke's Law (F = kx)
  • Basic knowledge of Newton's second law (F = ma)
  • Familiarity with elastic potential energy equations
  • Ability to perform unit conversions (e.g., kg to Newtons using 9.8 m/s²)
NEXT STEPS
  • Review the derivation of Hooke's Law and its applications in real-world scenarios.
  • Learn how to calculate elastic potential energy and its relationship with spring compression.
  • Explore the effects of varying mass on spring systems in different contexts.
  • Practice solving complex problems involving multiple masses and spring constants.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, engineers designing spring systems, and anyone interested in practical applications of Hooke's Law.

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Homework Statement



A 60 kg driver gets into an empty taptap to start the day's work. The springs compress 0.02 m. What is the effective spring constant of the spring system in the taptap?
using F=kx I got 2.94*10^4
Then
After driving a portion of the route, the taptap is fully loaded with a total of 25 people with an average mass of 60 kg per person. In addition, there are three 15 kg goats, five 3 kg chickens, and a total of 25 kg of bananas on their way to the market. Assume that the springs have somehow not yet compressed to their maximum amount. How much are the springs compressed?
I used the formula F=kx, solving for x, but i got the wrong answer (1.80*10^4) the answers turns out to be .5328. I just don't know how to get there.
For F i just multiplied each set of things times the number there was of them times the mass (kg) times 9.8 m/s^2 to get Newtong for each, then i divided that by the constant i found previously.

Homework Equations





The Attempt at a Solution


I used the formula F=kx, solving for x, but i got the wrong answer (1.80*10^4) the answers turns out to be .5328. I just don't know how to get there.
For F i just multiplied each set of things times the number there was of them times the mass (kg) times 9.8 m/s^2 to get Newtong for each, then i divided that by the constant i found previously.
 
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The work done by man in compressing the spring is equal to the gain in elastic energy of the spring.

mgx=0.5kx^2
solve this and you will get value of k
Rest is done using same equation.
 
i realized all i was doing wrong was the total mass of the taptap thanks anyways..
 

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