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3 years ago

A mass is oscillating up and down on a spring. In the above graph of

Physics

1 answer:

melomori [17]3 years ago

5 0

Answer:

Amplitude= 8 m

Explanation:

The Amplitude of a Wave

Sinusoidal Function refers to a mathematical curve with a smooth and periodic oscillation. Its name comes from the sine function and is characterized by the amplitude or the maximum displacement or distance moved by a point on a vibrating body measured from its equilibrium position.

To calculate the amplitude from a graph, we measure the maximum point and the minimum point the wave reaches. Then we subtract both values and divide the result by 2.

The shown wave in the figure has a maximum value of 8 m and a minimum value of -8 m. The distance from the maximum to the minimum is 8-(-8)= 16 m, thus the amplitude is 16/2= 8m.

Amplitude= 8 m

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A bowling ball with a momentum of 18kg-m/s strikes a stationary bowling pin. After the collision, the ball has a momentum of 13k

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$\theta$ = Angle the pin makes with the horizotal after getting hit by the ball

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$P_i=P_1\cos55^{\circ}+P_2\cos\theta\\\Rightarrow P_2\cos\theta=P_i-P_1\cos55^{\circ}\\\Rightarrow P_2\cos\theta=18-13\cos55^{\circ}\\\Rightarrow P_2\cos\theta=10.54\ \text{kg m/s}$

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$P_1\sin55=P_2\sin\theta\\\Rightarrow P_2\sin\theta=13\sin55^{\circ}\\\Rightarrow P_2\sin\theta=10.64\ \text{kg m/s}$

$(P_2\cos\theta)^2+(P_2\sin\theta)^2=P_2^2\\\Rightarrow P_2=\sqrt{10.54^2+10.64^2}\\\Rightarrow P_2=14.98\ \text{kg m/s}$

The pin's resultant velocity is $14.98\ \text{kg m/s}$

$P_2\sin\theta=10.64\\\Rightarrow \theta=sin^{-1}\dfrac{10.64}{14.98}\\\Rightarrow \theta=45.26^{\circ}$

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