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3 years ago

An object on a spring whose constant is 30. N/m

Physics

1 answer:

MrRa [10]3 years ago

3 0

The mass of the object is 0.0076 kg

Explanation:

The frequency of a mass-spring system (simple harmonic motion) is given by

$f=\frac{1}{2\pi}\sqrt{\frac{k}{m}}$

where

f is the frequency

k is the spring constant

m is the mass

For the mass-spring system in this problem, we know:

k = 30 N/m is the spring constant

f = 10 Hz is the frequency

Solving the equation for m, we find the mass:

$m=\frac{k}{(2\pi f)^2}=\frac{30}{(2\pi (10))^2}=0.0076 kg$

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In a 49 s interval, 595 hailstones strike a glass window of an area of 0.954 m at an angle of 25° to the window surface. Each ha

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Average force on the window: 0.32 N

Explanation:

The average force exerted on the window is given by Newton's second law

$F=\frac{\Delta p}{\Delta t}$

where

$\Delta p$ is the net change in momentum of the hailstones in a time interval of $\Delta t$

In order to find the change in momentum, we have to consider only the component of the hailstone's momentum perpendicular to the window, therefore:

$p_i =m u sin \theta$ is the initial momentum of one hailstone, with

m = 7 g = 0.007 kg is the mass

$u=4.5 m/s$ is the initial speed

$\theta=25^{\circ}$ is the angle with the window

The final momentum is

$p_f = mv sin \theta$

where

v = 4.5 m/s is the final speed (the collision is elastic so the speed is equal, while the direction changes)

$\theta=-25^{\circ}$ (after the rebound, the direction has changed)

So the change in momentum of 1 hailstone is

$\Delta p = mv sin(-25^{\circ})-mu sin(25^{\circ})=-2mu sin(25^{\circ})=-0.0266 kg m/s$

We are interested only in the magnitude, so

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There are 595 hailstones hitting the window in 49 s, so the total change in momentum is

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And therefore, the average force on the window is

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Learn more about force:

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3 0

3 years ago