Calculating Maximum Speed of a Child on a Swing | Simple Harmonic Motion

In summary, the maximum speed of the child on the swing can be calculated using conservation of energy. The child's potential energy is equal to their kinetic energy, so the equation mgh = 0.5mv^2 can be used to find the maximum speed. This cannot be solved using SHM equations since only the height is given. The book's answer is 3.2m/s.
  • #1
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I don't find this topic too difficult but I am really stuggling on a question (im sure its really simple though)

A child on a swing rises throught a height of 0.5m. Ignoring resistive energy losses, calculate the maximum speed of the child (the child doesn't increase/decrease swing height and take g=10m/s/s)

Please could someone tell me the method and the answers you get. (the book says 3.2m/s but i didn't get that)

Thanks.
 
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  • #2
Use conservation of energy.
 
  • #3
oh, how would you do that ? I thought it was to do with the SHM equations.
 
  • #4
The speed will be maximal when all of the original potential energy is converted to kinetic energy. The PE is given by mgh. The KE is 0.5mv^2.
You can't use the SHM equations here cause all you have is the height.
 

What is simple harmonic motion?

Simple harmonic motion (SHM) is a type of periodic motion in which an object oscillates back and forth around an equilibrium position due to a restoring force that is directly proportional to the displacement from the equilibrium position. It is a common phenomenon observed in many systems, such as pendulums, springs, and various types of waves.

What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x = A sin(ωt + φ), where x is the displacement from equilibrium, A is the amplitude (maximum displacement), ω is the angular frequency (related to the period T by ω = 2π/T), and φ is the phase constant (related to the initial conditions).

What is the difference between simple harmonic motion and periodic motion?

Simple harmonic motion is a type of periodic motion, but not all periodic motion is simple harmonic. Periodic motion refers to any motion that repeats itself after a fixed amount of time, while simple harmonic motion specifically refers to motion that follows the equation x = A sin(ωt + φ). Therefore, simple harmonic motion is a more specific type of periodic motion.

What is the relationship between simple harmonic motion and energy?

Simple harmonic motion involves the exchange of potential and kinetic energy. As the object moves towards the equilibrium position, it gains kinetic energy and loses potential energy. As it moves away from the equilibrium position, it gains potential energy and loses kinetic energy. This results in a constant total energy throughout the motion.

What factors affect the period of simple harmonic motion?

The period of simple harmonic motion is affected by the mass of the object, the spring constant, and the amplitude of the motion. A greater mass will result in a longer period, while a larger spring constant and smaller amplitude will result in a shorter period.

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