All categories

3 years ago

A mass of 240 grams oscillates on a horizontal frictionless surface at a frequency of 2.5 Hz and with amplitude of 4.5 cm.

Physics

1 answer:

mr_godi [17]3 years ago

5 0

Answer:

(a) The spring constant is 59.23 N/m

(b) The total energy involved in the motion is 0.06 J

Explanation:

Given;

mass, m = 240 g = 0.24 kg

frequency, f = 2.5 Hz

amplitude of the oscillation, A = 4.5 cm = 0.045 m

The angular speed is calculated as;

ω = 2πf

ω = 2 x π x 2.5

ω = 15.71 rad/s

(a) The spring constant is calculated as;

$\omega = \sqrt{\frac{k}{m} } \\\\\omega ^2 = \frac{k}{m} \\\\k = m\omega ^2\\\\where;\\\\k \ is \ the \ spring \ constant\\\\k = (0.24) \times (15.71)^2\\\\k = 59.23 \ N/m$

(b) The total energy involved in the motion;

E = ¹/₂kA²

E = (0.5) x (59.23) x (0.045)²

E = 0.06 J

You might be interested in

What type of pipe wrenches are designed for turning and holding where marring is not objectionable?

galina1969 [7]

The type of pipe wrenches which are designed to turn and hold where marring is not objectionable is known as the chain wrench.<span> It has two serrated which adjust and grip the pipe. </span>

5 0

3 years ago

A parachutist falls 50.0 m without friction. When the parachute opens, he slows down at a rate of 67 m/s*2. If he reaches the gr

KIM [24]

Answer:

3.49 seconds

3.75 seconds

-43200 ft/s²

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

$s=ut+\frac{1}{2}at^2\\\Rightarrow 50=0t+\frac{1}{2}\times 9.81\times t^2\\\Rightarrow t=\sqrt{\frac{50\times 2}{9.81}}\\\Rightarrow t=3.19\ s$

Time the parachutist falls without friction is 3.19 seconds

$v^2-u^2=2as\\\Rightarrow v=\sqrt{2as+u^2}\\\Rightarrow v=\sqrt{2\times 9.81\times 50+0^2}\\\Rightarrow v=31.32\ m/s$

Speed of the parachutist when he opens the parachute 31.32 m/s. Now, this will be considered as the initial velocity

$v=u+at\\\Rightarrow 11=31.32+9.81t\\\Rightarrow t=\frac{11-31.32}{-67}=0.3\ s$

So, time the parachutist stayed in the air was 3.19+0.3 = 3.49 seconds

$s=ut+\frac{1}{2}at^2\\\Rightarrow \frac{s}{2}=0t+\frac{1}{2}\times a\times t^2\\\Rightarrow \frac{s}{2}=\frac{1}{2}at^2$

$s=ut+\frac{1}{2}at^2\\\Rightarrow \frac{s}{2}=u1.1+\frac{1}{2}\times a\times 1.1^2$

Now the initial velocity of the last half height will be the final velocity of the first half height.

$v=u+at\\\Rightarrow v=at$

Since the height are equal

$\frac{1}{2}at^2=u1.1+\frac{1}{2}\times a\times 1.1^2\\\Rightarrow \frac{1}{2}at^2=at1.1+\frac{1}{2}\times a\times 1.1^2\\\Rightarrow 0.5t^2-1.1t-0.605=0\\\Rightarrow 500t^2-1100t-605=0$

$t=\frac{11\left(1+\sqrt{2}\right)}{10},\:t=\frac{11\left(1-\sqrt{2}\right)}{10}\\\Rightarrow t=2.65, -0.45$

Time taken to fall the first half is 2.65 seconds

Total time taken to fall is 2.65+1.1 = 3.75 seconds.

When an object is thrown with a velocity upwards then the velocity of the object at the point to where it was thrown becomes equal to the initial velocity.

$v^2-u^2=2as\\\Rightarrow a=\frac{v^2-u^2}{2s}\\\Rightarrow a=\frac{0^2-240^2}{2\times \frac{8}{12}}\\\Rightarrow a=-43200\ ft/s^2$

Magnitude of acceleration is -43200 ft/s²

5 0

3 years ago

Ana wonders how light can affect a mystery material. The table below shows what happens when different types of light hit the my

vivado [14]

The light can definitely change the mystery material. This can occur through a change in temperature or color (option C).

A material is affected by light mainly if the material absorbs the light. Based on the chart, we know this mystery material can absorb two types of light:

Red light.
Yellow light.

Moreover, this phenomenon can lead to two main changes:

Change in temperature: Light affects materials by increasing their temperature of these. A common example is the way the temperature of an object increases if it is exposed to sunlight.
Change in color: Some materials react to light by changing their color.

Based on this, the material can change its color or temperature.

Note: This question is incomplete; here is the missing part:

A. Yes, but the mystery material can change in only one way, such as by getting warm, because all the light that a material absorbs will affect that material in the same way.

B. No. The mystery material can’t change because the light is not a physical thing. Light cannot change physical things like the mystery material.

C. Yes and the mystery material can change in one or two different ways, such as by getting warm and/or changing color, because different types of light can cause different changes to a material when they are absorbed.

D. There is no way to know whether the mystery material will change or not.

Learn more about sunlight in: brainly.com/question/1603783

3 0

3 years ago

A 5kg rock and a 10kg rock are dropped from a height of 10m?

fredd [130]

Look out below ! You should step nimbly to one side, to avoid being hit by one or the other of those hazardous weight objects when they arrive (at the same time).

5 0

3 years ago

All the scientific theories used to explain the formation of the solar system are. . outdated. . imaginative. . non-testable. .

maria [59]

The correct answer for the statement “All the scientific theories used to explain the formation of the solar system are non-testable”. The answers outdated, imaginative and unacceptable are wrong. These theories are not proven and yet are not tested due to the complexity.

3 0

3 years ago

Read 2 more answers