Ch 10: Interactions and Potential Energy

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 10: Interactions and Potential Energy

Problem 10

Chapter 10, Problem 10

The spring in FIGURE EX10.21a is compressed by 10 cm. It launches a block across a frictionless surface at 0.50 m/s. The two springs in Figure EX10.21b are identical to the spring of Figure EX10.21a. They are compressed by the same 10 cm and launch the same block. What is the block's speed now?

Verified step by step guidance

Identify the energy transformation involved: Initially, the potential energy stored in the compressed spring is converted into the kinetic energy of the block as it is launched.

Calculate the initial potential energy stored in the spring using the formula for spring potential energy, PE = 0.5 * k * x^2, where 'k' is the spring constant and 'x' is the compression distance.

Determine the kinetic energy of the block using the formula KE = 0.5 * m * v^2, where 'm' is the mass of the block and 'v' is its velocity. Use the velocity given for the single spring setup to find the kinetic energy.

For the setup with two springs, assume that the potential energy stored in the system when both springs are compressed is twice that of the single spring, since both springs are identical and compressed by the same amount.

Use the conservation of energy principle to equate the total potential energy from the two springs to the kinetic energy of the block and solve for the new velocity 'v' of the block.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Hooke's Law

Hooke's Law states that the force exerted by a spring is directly proportional to its displacement from the equilibrium position, expressed as F = -kx, where k is the spring constant and x is the displacement. This principle is crucial for understanding how the potential energy stored in a compressed spring is converted into kinetic energy when the spring is released.

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In this scenario, the potential energy stored in the compressed spring is converted into kinetic energy of the block as it is launched. This concept allows us to analyze the relationship between the initial and final speeds of the block.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion, calculated using the formula KE = 1/2 mv², where m is the mass and v is the velocity of the object. Understanding kinetic energy is essential for determining how the speed of the block changes when launched by the springs, especially when comparing the effects of multiple springs acting on the same mass.

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