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suter [353]
3 years ago
13

A child's toy consists of a spherical object of mass 50 g attached to a spring. One end of the spring is fixed to the side of th

e baby's crib so that when the baby pulls on the toy and lets go, the object oscillates horizontally with a simple harmonic motion. The amplitude of the oscillation is 6 cm and the maximum velocity achieved by the toy is 3.2 m/s . What is the potential energy (U) of the toy when the spring is compressed 4.4 cm from its equilibrium position? *I found the KE, but need help on PE*
Physics
1 answer:
Artemon [7]3 years ago
6 0

Answer:

0.14 J

Explanation:

The maximum velocity is the amplitude times the angular frequency.

vmax = Aω

ω = vmax / A

ω = (3.2 m/s) / (0.06 m)

ω = 53.3 rad/s

For a spring-mass system:

ω = √(k / m)

ω² = k / m

k = ω²m

k = (53.3 rad/s)² (0.050 kg)

k = 142 N/m

The elastic potential energy is:

EE = ½ kx²

EE = ½ (142 N/m) (0.044 m)²

EE = 0.14 J

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Marco is conducting an experiment. He knows the wave that he is working with has a wavelength of 32.4 cm. If he measures the fre
vekshin1

This question is incomplete; here is the complete question:

Marco is conducting an experiment. He knows the wave that he is working with has a wavelength of 32.4 cm. If he measures the frequency as 3 hertz, which statement about the wave is accurate?

A. The wave has traveled 32.4 cm in 3 seconds.

B. The wave has traveled 32.4 cm in 9 seconds.

C. The wave has traveled 97.2 cm in 3 seconds.

D. The wave has traveled 97.2 cm in 1 second.

The answer to this question is D. The wave has traveled 97.2 cm in 1 second.

Explanation:

The frequency of a wave, which is in this case 3 hertz, represents the number of waves that go through a point during 1 second. According to this, if the frequency of the wave is 3 hertz this means in 1 second there were 3 waves. Moreover, if you multiply the wavelength (32.4cm) by the frequency (3) you will know the distance the wave traveled in 1 second: 32.4 x 3 =  97.2 cm. This makes option D the correct one as the distance in 1 second was 97.2 cm.

8 0
3 years ago
HELP I WILL MARK AS BRAINLIEST!
trapecia [35]

Answer:

it is c

Explanation:

8 0
3 years ago
A Viking ship roller coaster at the fair has a mass of 36,000 kg. If at its peak it reaches a height of 20 m off the ground, how
adell [148]

Answer:

7056 kJ

Explanation:

Given that,

Mass of a ship roller coaster is 36,000 kg.

It reaches a height of 20 m off the ground

We need to find the gravitational potential energy does it have. The formula for the gravitational potential energy ios given by :

E = mgh

g is acceleration due to gravity

E = 36,000 kg × 9.8 m/s² × 20 m

= 7056000 J

or

E = 7056 kJ

So, it will have 7056 kJ of gravitational potential energy.

8 0
3 years ago
A horizontal beam of electrons initially moving at 4.0×10^7 m/s is deflected vertically by the vertical electric field between o
givi [52]

Answer:

1.77\times 10^{-7}\ C/m^2

0.000439077936334 m

Explanation:

q = Charge of electron = 1.6\times 10^{-19}\ C

E = Electric field = 2\times 10^{4}\ N/C

\epsilon_0 = Permittivity of free space = 8.85\times 10^{-12}\ F/m

d = Distance between plates = 2 cm (assumed)

m = Mass of electron = 9.11\times 10^{-31}\ kg

The beam consists of electrons which means it has negative charge this means the upper plates will be positive and the lower plate will be negative.

The direction is upper to lower lower plate.

\epsilon_0 = Permittivity of free space = 8.85\times 10^{-12}\ F/m

Electric flux is given by

\phi=\epsilon_0E\\\Rightarrow \phi=8.85\times 10^{-12}\times 2\times 10^{4}\\\Rightarrow \phi=1.77\times 10^{-7}\ C/m^2

The charge per unit area on the plates is 1.77\times 10^{-7}\ C/m^2

Deflection is given by

s=\dfrac{1}{2}\dfrac{qE}{m}(\dfrac{d}{v})^2\\\Rightarrow s=\dfrac{1}{2}\dfrac{1.6\times 10^{-19}\times 2\times 10^4}{9.11\times 10^{-31}}(\dfrac{0.02}{4\times 10^7})^2\\\Rightarrow s=0.000439077936334\ m

The deflection is 0.000439077936334 m

7 0
3 years ago
5. A stream of air at 12 bar and 900 K is mixed with another stream of air at 2 bar and 400 K with 2 times the mass flowrate. If
Softa [21]

Answer:

The anserrs to the question are

(a)  The temperature would be 566.67  K and

(b) The pressure of the resulting air stream is 14 bar

Explanation:

Here the two streams of gases meet ad form a single stream

The steady-flow energy equation can be implemented at the mixing point of the to streams as follows

mₐhₐ₁ + mₙ hₙ₁ + Q° + W° = mₐhₐ₂ + mₙhₙ₂

Where the flow is adiabatic, we have

Q = 0 and  W = 0  hence

mₐhₐ₁ + mₙ hₙ₁ = mₐhₐ₂ + mₙhₙ₂ where h = cp×T we have

mₐcpₐ×Tₐ + mₙcpₙ×Tₙ  = mₐcpₐ×T + mₐcpₙ×T

Therefore the final temperature T is given by

T = \frac{m_ac_{pa}T_a + m_nc_{pn}T_n}{m_ac_{pa} + m_nc_{pn}}  for the same kind of gas cpₐ =cpₙ therefore

T = \frac{m_aT_a + m_nT_n}{m_a + m_n} where mₐ and mₙ are mass flow rate

Therefore we have where Tₐ = = 900 K and Tₙ = 400 K and mₙ = 2mₐ gives

T = \frac{m_a*900 + 2*m_a*400}{m_a + 2*m_a} = T = \frac{900 + 800}{1 + 2} = 1700/3 = 566.67 K  

From Dalton's law, the total pressure of a mixture of gases is equal to the sum of the partial pressures of the components of the mixture

Therefore the total pressure of the combined stream = pₐ + pₙ = p

= 12 bar + 2 bar = 14 bar

Stream pressure = 14 bar

4 0
3 years ago
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