Can somebody please explain to me how the acceleration in simple hormonic motion is proportional to the displacement..

Answers

Answer 1

Answer: When you graph simple harmonic motion in an acceleration versus displacement graph, the graph at any point would be linear. The graph would also pass through the origin giving proportionality of acceleration to negative displacement. Definition of proportionality neglects the negative value of the displacement so therefore acceleration is proportional to displacement. The acceleration of the motion is always directed towards equilibrium and so at maximum displacement, there would be greatest negative acceleration and vise versa.At the origin, the displacement would be zero and acceleration would also be zero

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Which of the following describes volumeA.the number of particles or amount of matter
B.the amount of space that matter ocupies
C.how fast the particles are moving
D.amount of massin a certain place

Answers

B.the amount of space that matter ocupies

A student releases a block of mass m at the top of a slide of height h1. the block moves down the slide and off the end of the table of height h2, landing on the floor a horizontal distance d from the edge of the table. Friction and air resistance are negligible. The overall height H of the setup is determined by the height of the room. Therefore, if h1 is increased, h2 must decrease by the same amount so that the sum h1+h2 remains equal to H. The student wants to adjust h1 and h2 to make d as large as possible.A) 1) Without using equations, explain why making h1 very small would cause d to be small, even though

h2 would be very large?
2) Without using equations, explain why making h2 very small would cause d to be small, even though
h1 would be large

B) Derive an equation for d in terms of h1, h2, m, and physical constants as appropriate.

Answers

(A)

(1) The reason for making $h_(1)$ very small is due to smaller value of horizontal component of launch velocity.

(2) The reason for making $h_(2)$ very small is due to smaller value of time of flight.

(B) The distance (d) covered by the block is $2\sqrt{h_(1)h_(2)}$ .

Given data:

The mass of block is, m.

The height of table from the top of slide is, $h_(1)$ .

The height of table at the end of slide is, $h_(2)$ .

The height of room is, H.

(A)

(1)

If the launch velocity of the block is v, then its horizontal component is very small, due to which adjusting the height $h_(1)$ to be very small will cause the d to be small.

(2)

The height $h_(2)$ is dependent on the time of flight, and since the time of flight taken by the block to get to the floor is very less, therefore the block will not get sufficient time to accomplish its horizontal motion. That is why making $h_(2)$ very small will cause d to be smaller.

(B)

The expression for the distance covered by the block is,

$v=(d)/(t)\nd = v * t$ ..............................(1)

Here, v is the launch speed of block and t is the time of flight.

The launch speed is,

$v^(2)=u^2+2gh_(1)\nv=\sqrt{u^2+2gh_(1)}\nv=\sqrt{0^2+2gh_(1)}\nv=\sqrt{2gh_(1)}$

And the time of flight is,

$h_(2)=ut+(1)/(2)gt^(2)\nh_(2)=0 * t+(1)/(2)gt^(2)\nh_(2)=0+(1)/(2)gt^(2)\nt=\sqrt(2h_(2))/(g)$

Substituting the values in equation (1) as,

$d = v * t\nd = \sqrt{2gh_(1)}* \sqrt(2 h_(2))/(g)}\nd=2\sqrt{h_(1)h_(2)}$

Thus, the distance (d) covered by the block is $2\sqrt{h_(1)h_(2)}$ .

Learn more about the time of flight here:

brainly.com/question/17054420?referrer=searchResults

A1) The reason why making h₁ very small would cause d to be small is; Because the horizontal component of the launch velocity would be very small.

A2) The reason why making h₂very small would cause d to be small is;

Because the time of flight it will take the object to get to the floor would be very small and as a result, the object would not possess enough time to move horizontally before the vertical motion.

B) The equation for d in terms of h₁ and h₂ is;

d = 2√(h₁ × h₂)

A) 1) The reason why making h₁ very small would cause d to be small is because the horizontal component of the launch velocity would be very small.

A) 2) The reason why making h₂ very small would cause d to be small is because the time of flight it will take the object to get to the floor would be very small and as a result, the object would not possess enough time to move horizontally before the vertical motion.

B) Formula for Launch Velocity is;

V = √(2gh₁)

h₁ was used because the top of the slide from where the student released the block has a height of h₁.

Also, the time it takes to fall which is time of flight is given by the formula;

t = √(2h₂/g)

h₂ was used because the height of the table the object is on before falling is h₂.

Now, we know that d is distance from edge of the table and formula for distance with respect to speed and time is;

distance = speed × time

Thus;

d = √(2gh₁) × √(2h₂/g)

g will cancel out and this simplifies to give;

d = 2√(h₁ × h₂)

Read more at; brainly.com/question/20427663

A substance has a melting point of 0 degrees celsius and a boiling point of 100 degrees celsius. The substance is most likely a.) water
b.) hydrogen
c.) gold
d.) table salt

Answers

The correct answer is A. The parameters laid out here describe water,which has a melting point of 0 degrees Celsius and a boiling point of100 degrees Celsius. These descriptors are not true of any of thealternative answers.

a car travelling at 36 km/hr due north turns west in 5 s under constant acceleration and maintains the same speed. the acceleration of the car is

Answers

If acceleration is constant we calculate it from the formula:
a= $(v)/(t)$
v=36 $(km)/(h)$
t=5s
We convert units:
t=5s= $(1)/(12)$ h
a= $(36)/( (1)/(12))$ =432 $(km)/(h²)$ =0,033333333333333 $(m)/( s^(2) )$

The blue end of the visible color spectrum has wavelengths, and the red end has wavelengths.

Answers

Answer: Blue end has shorter wavelength and red end has longer wavelengths.

Explanation:

Visible region consists of Violet, Indigo, Blue, Green, Yellow, Orange and Red. These colors are arranged in the order of increasing wavelengths which means that blue region has shorter wavelength and as we move towards red region, the wavelength of light increases.

Blue region has shorter wavelength and higher frequency whereas red region has longer wavelength and smaller frequency.

Frequency and wavelength follow inverse relation.

$\nu\propto (1)/(\lambda)$

Answer: Blue end has shorter wavelength and red end has longer wavelengths.

Explain the difference between mass and weight for objects on earth and on the mooon

Answers

Explanation:

The amount of matter contained inside a body is called its mass while the weight of a body is the gravitational force with which it is attracted towards the earth.

Weight, W = mg

m is the mass and g is acceleration due to gravity

The mass of the object on the moon remains the same but the weight of the body is reduced to one sixth. This is because the moon's gravity is less than the earth's gravity.

Hence, this is the main difference in the weight of the object on the earth and on the moon.

Mass stays the same no matter what, weight however is affected by gravity and will be different on the moon than on earth.

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