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Fittoniya [83]
3 years ago
14

A metal ball attached to a spring moves in simple harmonic motion. The amplitude of the ball's motion is 11.0 cm, and the spring

constant is 5.50 N/m. When the ball is halfway between its equilibrium position and its maximum displacement from equilibrium, its speed is 27.2 cm/s.(a) What is the mass of the ball (in kg)?(b) What is the period of oscillation (in s)?(c) What is the maximum acceleration of the ball? (Enter the magnitude in m/s2.)
Physics
1 answer:
german3 years ago
7 0

Answer:

a)0.674 kg b) 2.2 s c) 0.9 m/s²

Explanation:

The amplitude of the ball (xo) = 11.0cm, half way between its equilibrium point its maximum displacement x = 11 cm / 2 = 5.5 cm = 5.5 / 100 in meters = 0.055 meters, speed at this point = 27.2 cm /s = (27.2 / 100) in m/s = 0.272 m/s,

spring constant K = 5.5 N/m

a) The mass of the ball (m) can be calculated using the formula below

v =√ (x²o - x²)K/m

make m subject of the formula

v² = (xo² - x²) K/m

m = K ( xo² - x²) / v²

m = 0.674kg

b) The period of the oscillation can be calculated by the following formula

T = 2π√ (m /K)

substitute the values into the formula

T = 2 × 3.142 × √ (0.674/ 5.5) = 2.2s

c) The maximum acceleration of the ball which occurs at the maximum displacement of the ball can be calculated by the following formula

a = K / m × x ( maximum displacement of the body) = 5.5 / 0.674 × 0.11 = 0.9 m/s²

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Potential energy plus kinetic energy are combined to form mechanical energy. According to the principle of mechanical energy conservation, mechanical energy is constant in an isolated system when only conservative forces are acting on it. Potential energy increases when an object moves in the opposite direction of a conservative net force. Kinetic energy also changes as an object's speed, not velocity, changes. However, nonconservative forces, such as frictional forces, will always be present in real systems; however, if these forces are of minimal magnitude, mechanical energy changes little, making the idea of its conservation a reasonable approximation.

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