How Do You Calculate the Spring Constant for a Toy Car Accelerated by a Spring?

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SUMMARY

The spring constant for a 2.8 kg toy car accelerated to 4.5 m/s over a distance of 5.3 cm can be calculated using Hooke's Law and the work-energy principle. The correct formula to use is F = (1/2)kx², where F is the force exerted by the spring, k is the spring constant, and x is the displacement. By applying the kinetic energy formula and rearranging the equations, the spring constant can be determined accurately.

PREREQUISITES
  • Understanding of Hooke's Law
  • Basic knowledge of kinetic energy calculations
  • Familiarity with Newton's second law of motion
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the derivation of Hooke's Law and its applications
  • Learn how to calculate kinetic energy and relate it to work done by a spring
  • Explore examples of spring constant calculations in physics problems
  • Investigate the effects of mass and acceleration on spring dynamics
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and spring dynamics, as well as educators looking for practical examples of applying Hooke's Law in problem-solving scenarios.

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A 2.8 kg toy car at rest on a horizontal surface is accelerated by a spring to 4.5 m/s in a distance of 5.3 cm. What is the spring constant of the spring?

Hello, I was working on this problem in my homework but my professor hardly went over the spring constant in lecture. I was working on the problem but keep coming up with the incorrect answer.

Is starting off with F=(1/2)kx^2 the correct way to start off with this sort of problem?
 
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