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Consider two spring-loaded toy cannons, which make the same angle with the horizontal and fire...

Question:

Consider two spring-loaded toy cannons, which make the same angle with the horizontal and fire projectiles of the same mass. The spring of cannon 1 has a spring constant of 20N/m, and it is compressed 5cm. The spring of cannon 2 has k=10N/m, and it is compressed 10cm. Disregard air resistance. Will one of the cannons fire farther? Or will they have the same range? Or is there not enough info to tell?

Hooke's Law:

Hooke's law is defined as a law that states that the restoring force of a spring will be proportional to the deformation experimented by it. For small elongations, the spring will try to recover its original form if the load or force that causes the elongation is removed.

  • Spring constant: The spring constant is defined as a factor that determines the stiffness of a spring. The bigger this value, the more force is required to compress the spring.

Equation:

The restoring force on a spring can be calculated through the following formula:

$$F=-Kx $$

Where:

  • F is the force
  • K is the spring constant
  • x is the deformation

Answer and Explanation:

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We can determine which cannon will travel farther if we determine which projectile will leave the spring with the biggest velocity. We can use the...

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Hooke's Law & the Spring Constant: Definition & Equation

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Chapter 4 / Lesson 19
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After watching this video, you will be able to explain what Hooke's Law is and use the equation for Hooke's Law to solve problems. A short quiz will follow.


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