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3 years ago

What is the toy's total energy at any point of its motion? Express your answer with the appropriate units.]

Physics

1 answer:

suter [353]3 years ago

6 0

The complete question is as follows:

A 0.150-kg toy is undergoing SHM on the end of a horizontal spring with force constant k = 300 N/m. When the toy is 0.0120 m from its equilibrium position, it is observed to have a speed of 0.400 m/s.

Answer:

The correct answer is 0.034 J.

Explanation:

Given :

mass of the toy is m = 0.15 kg.

The force constant of restoring force k = 300 Nm⁻¹

When the position of the toy from the equilibrium is x = 0.012m, then the

speed of the toy vx = 0.4m s

The total mechanical energy in SHM is given by

E= 1/2 (mv²+ kx²) = 1/2 kA²

(here, m = mass of the object, vx = velocity, k = force constant

of restoring force, and A = amplitude of SHM.)

Hence by substituting the numerical values in equation 1, we get

$E= \frac{1}{2} (0.15* 0.4) + \frac{1}{2} (300* 0.012)$

= 0.034 J

Thus, the correct answer is 0.034 J.

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That ratio is 2 .

<h3>What is ratio?</h3>

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8 0

1 year ago

Two particles with masses 2m and 9m are moving toward each other along the x axis with the same initial speeds vi. Particle 2m i

s2008m [1.1K]

Answer:

The final speed for the mass 2m is $v_{2y}=-1,51\ v_{i}$ and the final speed for the mass 9m is $v_{1f} =0,85\ v_{i}$ .

The angle at which the particle 9m is scattered is $\theta = -66,68^{o}$ with respect to the - y axis.

Explanation:

In an elastic collision the total linear momentum and the total kinetic energy is conserved.

<u>Conservation of linear momentum:</u>

Because the linear momentum is a vector quantity we consider the conservation of the components of momentum in the x and y axis.

The subindex 1 will refer to the particle 9m and the subindex 2 will refer to the particle 2m

$\vec{p}=m\vec{v}$

$p_{xi} =p_{xf}$

In the x axis before the collision we have

$p_{xi}=9m\ v_{i} - 2m\ v_{i}$

and after the collision we have that

$p_{xf} =9m\ v_{1x}$

In the y axis before the collision $p_{yi} =0$

after the collision we have that

$p_{yf} =9m\ v_{1y} - 2m\ v_{2y}$

$p_{xi} =p_{xf} \\7m\ v_{i} =9m\ v_{1x}\Rightarrow v_{1x} =\frac{7}{9}\ v_{i}$

then

$p_{yi} =p_{yf} \\0=9m\ v_{1y} -2m\ v_{2y} \\v_{1y}=\frac{2}{9} \ v_{2y}$

<u>Conservation of kinetic energy:</u>

$\frac{1}{2}\ 9m\ v_{i} ^{2} +\frac{1}{2}\ 2m\ v_{i} ^{2}=\frac{1}{2}\ 9m\ v_{1f} ^{2} +\frac{1}{2}\ 2m\ v_{2f} ^{2}$

$\frac{11}{2}\ m\ v_{i} ^{2} =\frac{1}{2} \ 9m\ [(\frac{7}{9}) ^{2}\ v_{i} ^{2}+ (\frac{2}{9}) ^{2}\ v_{2y} ^{2}]+ m\ v_{2y} ^{2}$

Putting in one side of the equation each speed we get

$\frac{25}{9}\ m\ v_{i} ^{2} =\frac{11}{9}\ m\ v_{2y} ^{2}\\v_{2y} =-1,51\ v_{i}$

We know that the particle 2m travels in the -y axis because it was stated in the question.

Now we can get the y component of the speed of the 9m particle:

$v_{1y} =\frac{2}{9}\ v_{2y} \\v_{1y} =-0,335\ v_{i}$

the magnitude of the final speed of the particle 9m is

$v_{1f} =\sqrt{v_{1x} ^{2}+v_{1y} ^{2} }$

$v_{1f} =\sqrt{(\frac{7}{9}) ^{2}\ v_{i} ^{2}+(-0,335)^{2}\ v_{i} ^{2} }\Rightarrow \ v_{1f} =0,85\ v_{i}$

The tangent that the speed of the particle 9m makes with the -y axis is

$tan(\theta)=\frac{v_{1x} }{v_{1y}} =-2,321 \Rightarrow\theta=-66,68^{o}$

As a vector the speed of the particle 9m is:

$\vec{v_{1f} }=\frac{7}{9} v_{i} \hat{x}-0,335\ v_{i}\ \hat{y}$

As a vector the speed of the particle 2m is:

$\vec{v_{2f} }=-1,51\ v_{i}\ \hat{y}$

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3 years ago

On a frictionless plane inclined at angle 303. The box is connected via a cord of negligible mass to a box of laundered money (m

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Answer:

T = 1.73 kg

Explanation:

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Wx = W sin θ

Wy = W cos θ

Wx = 2.0 ain 60

Wx = 1.73 kg

Wy = 2.0 cos 60

Wy = 1.0 kg

Y Axis

N-Wy = 0

X axis

T- Wx = 0

T = Wx

T = 1.73 kg

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3 years ago

If 4.00 ✕ 10−3 kg of gold is deposited on the negative electrode of an electrolytic cell in a period of 2.73 h, what is the curr

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Explanation:

Below is an attachment containing the solution.

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4 years ago

Which of these orders has the structure of the universe from the smallest to largest?

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Answer:

From largest to smallest they are: Universe, galaxy, solar system, star, planet, moon and asteroid.

Explanation:

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2 years ago