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3 years ago

8

A cube made Of an unknown material has a height of 9 symeters the mass of this cube is 3645 g. calculate the density of this cub

e given this information

1 answer:

kherson [118]3 years ago

8 0

Answer: $5 \frac{g}{cm^{3}}$

Explanation:

The density $\rho$ of a material is given by:

$\rho=\frac{m}{V}$ (1)

Where:

$m=3645 g$ is the mass of the cube

$V$ is the volume of the cube

Now, the volume of a cube is equal to the length $L$ of its edge to the power of 3:

$V=L^{3}$ (2)

If we know $L=9 cm$ , the volume of this cube is:

$V=(9 cm)^{3}=729 cm^{3}$ (3)

Substituting (3) in (1):

$\rho=\frac{3645 g}{729 cm^{3}}$ (4)

$\rho=5 \frac{g}{cm^{3}}$ This is the density of the cube

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g A 1.5-kg mass attached to spring with a force constant of 20.0 N/m oscillates on a horizontal, frictionless track. At t = 0, t

jok3333 [9.3K]

Answer:

(a) f = 0.58Hz

(b) vmax = 0.364m/s

(c) amax = 1.32m/s^2

(d) E = 0.1J

(e) x(t)=0.1m*cos(2π(0.58s^{-1})t)

Explanation:

(a) The frequency of the oscillation, in a spring-mass system, is calculated by using the following formula:

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

k: spring constant = 20.0N/m

m: mass = 1.5kg

you replace the values of m and k for getting f:

$f=\frac{1}{2\pi}\sqrt{\frac{20.0N/m}{1.5kg}}=0.58s^{-1}=0.58Hz$

The frequency of the oscillation is 0.58Hz

(b) The maximum speed is given by the following relation:

$v_{max}=\omega A=2\pi f A$ (2)

A: amplitude of the oscillations = 10.0cm = 0.10m

$v_{max}=2\pi (0.58s^{-1})(0.10m)=0.364\frac{m}{s}$

The maximum speed of the mass is 0.364 m/s.

The maximum speed occurs when the mass passes trough the equilibrium point of the oscillation.

(c) The maximum acceleration is given by the following formula:

$a_{max}=\omega^2A=(2\pi f)^2 A$

$a_{max}=(2\pi (0.58s^{-1}))(0.10m)=1.32\frac{m}{s^2}$

The maximum acceleration is 1.32 m/s^2

The maximum acceleration occurs where the elastic force is a maximum, that is, where the mass is at the maximum distance from the equilibrium point, that is, the acceleration.

(d) The total energy of the system is calculated with the maximum potential elastic energy:

$E=\frac{1}{2}kA^2=\frac{1}{2}(20.0N/m)(0.10m)^2=0.1J$

The total energy is 0.1J

(e) The displacement as a function of time is:

$x(t)=Acos(\omega t)=Acos(2\pi ft)\\\\x(t)=0.1m\ cos(2\pi(0.58s^{-1})t)$

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2 years ago

In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy without the aid of a pole.

Fiesta28 [93]

Answer:

6.0 m/s

Explanation:

According to the law of conservation of energy, the total mechanical energy (potential, PE, + kinetic, KE) of the athlete must be conserved.

Therefore, we can write:

$KE_i+PE_i =KE_f+PE_f$

or

$\frac{1}{2}mu^2+0=\frac{1}{2}mv^2+mgh$

where:

m is the mass of the athlete

u is the initial speed of the athlete (at the bottom)

0 is the initial potential energy of the athlete (at the bottom)

v = 0.80 m/s is the final speed of the athlete (at the top)

$g=9.8 m/s^2$ is the acceleration due to gravity

h = 1.80 m is the final height of the athlete (at the top)

Solving the equation for u, we find the initial speed at which the athlete must jump:

$u=\sqrt{v^2+2gh}=\sqrt{0.80^2+2(9.8)(1.80)}=6.0 m/s$

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3 years ago

A boat moves up and down as water waves pass under the boat. If the amplitude of the wave gets bigger, then

xeze [42]

The anwser is A or D

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2 years ago

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Infer the effect of deforestation on the carrying capacity of the Amazon rainforest.

RUDIKE [14]

Answer:

More than 20% of the amazon has been destroyed, affects biodiversity.

Explanation:

The biggest issues that the amazon is facing is the deforestation and it involves the clearing of land areas for logging, farming, and other land-use changes.

Effects that are seen are droughts, floods, destruction of habitats of flora and fauna along with the valuable services of the ecosystem.

This leads to a decrease in the carrying capacity of the species and the decline of the essential resources that are necessary to survive.

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Explain the meaning and use of the following acronyms: HELIOS, Exo-FMS, HAZMAT, NIRSpec.

adelina 88 [10]

Answer:

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Explanation:

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1 year ago