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Butoxors [25]
3 years ago
11

A force of 960 newtons stretches a spring 4 meters. A mass of 60 kilograms is attached to the end of the spring and is initially

released from the equilibrium position with an upward velocity of 6 m/s. Find the equation of motion.
Physics
1 answer:
Drupady [299]3 years ago
4 0

Answer:

x(t) = - 6 cos 2t

Explanation:

Force of spring = - kx

k= spring constant

x= distance traveled by compressing

But force = mass × acceleration

==> Force = m × d²x/dt²

===> md²x/dt² = -kx

==> md²x/dt² + kx=0   ------------------------(1)

Now Again, by Hook's law

Force = -kx

==> 960=-k × 400

==> -k =960 /4 =240 N/m

ignoring -ve sign k= 240 N/m

Put given data in eq (1)

We get

60d²x/dt² + 240x=0

==> d²x/dt² + 4x=0

General solution for this differential eq is;

x(t) = A cos 2t + B sin 2t   ------------------------(2)

Now initially

position of mass spring

at time = 0 sec

x (0) = 0 m

initial velocity v= = dx/dt=  6m/s

from (2) we have;

dx/dt= -2Asin 2t +2B cost 2t = v(t) --- (3)

put t =0 and dx/dt = v(0) = -6 we get;

-2A sin 2(0)+2Bcos(0) =-6

==> 2B = -6

B= -3

Putting B = 3 in eq (2) and ignoring first term (because it is not possible to find value of A with given initial conditions) - we get

x(t) = - 6 cos 2t

==>  

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nordsb [41]

Answer:

During an earthquake, seismic waves travels through the Earth's interior as body or p waves.

Explanation:

If neither of the bold words look familiar from your lesson feel free to ignore this answer

4 0
3 years ago
Which of the following is not an indication of a chemical reaction? a substance dissolves formation of a precipitate color chang
SVETLANKA909090 [29]

a substance dissolves.  


like adding a soluble salt to water, it just dissolves, i.e dissociates homogeneously as water is able to dissociate salts (ionic compounds) into its ions. (it can also dissociate other non-ionic compounds like HCL)  


the salt still remains chemically as a salt and is unchanged chemically thus it is not an indication of a chemical reaction as no chemical reaction has taken place.  


the formation of a precipitate is a chemical reaction because a new substance (i.e new chemical) is formed. For example adding aqueous sodium hydroxide into an aqueous solution with CU2+ cations will form a blue precipitate (that is copper (II) hydroxide which is insoluble, hence it precipitates). Since a new chemical is formed, a chemical reaction has taken place and thus indicates a chemical reaction.  


color change... im not sure but usually a color change will only occur when a new substance is formed. Like iron corrodes (i.e rust) slowly in moist air to form hydrated iron (III) oxide that is rust. (brown color).  


usually adding a mixture to a mixture has little energy change, i.e little heat taken in by the reaction mixture or little heat given out by the reaction mixture. Whereas when a new substance is formed, there is usually noticeable energy change like the container gets colder or hotter (without heat being supplied of course). For example dissolving basic oxides into water releases energy ( more energy released than gained = exothermic reaction).  


i think that should be the answer... hope it helped :D

4 0
3 years ago
Read 2 more answers
Which of the following is an exercise myth?
Margaret [11]
The answere is No pain, no gain
8 0
3 years ago
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Stan does 178 J of work lifting himself 0.5 m. What is Stan’s mass? The acceleration of gravity is 9.8 m/s 2 . Answer in units o
Rom4ik [11]
Work= (force)(distance)
178= m(9.81)x0.5
178=m(4.905)
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4 0
3 years ago
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A camera takes a properly exposed photo with a 4.0 mm diameter aperture and a shutter speed of 1/1000 s. If the photographer foc
hoa [83]

Answer:

option E

Explanation:

given,

diameter = 4 mm

shutter speed = 1/1000 s

diameter of aperture = ?

shutter speed = 1/250 s

exposure time to the shutter time

E V = log_2(\dfrac{N^2}{t})

N is the diameter of the aperture and t is the time of exposure

now,

log_2(\dfrac{N^2}{t_1})=log_2(\dfrac{N^2}{t_2})

\dfrac{N_1^2}{t_1}=\dfrac{N_2^2}{t_2}

inserting all the values

\dfrac{4^2}{1000}=\dfrac{N_2^2}{250}

      N₂² = 4

      N₂ = 2 mm

hence , the correct answer is option E

4 0
3 years ago
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