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3 years ago

Which equation can be used to model simple harmonic motion

Physics

1 answer:

mixer [17]3 years ago

8 0

Answer:x(t)= Acos(wt)

Explanation:

According to Newton's 2nd law,a particle of mass m acted on by a force is given by:Fs=-kx

Where x is displacement from equilibrium

K = spring constant

Therefore X(t) = Acos(2pit/T)

X(t)= Acos(wt)

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The total energy of a block—spring system is 0.18 J. The amplitude is 14.0 cm and the maximum speed is 1.25 m/s. Find: (a) the m

algol13

a) The mass is 0.23 kg

b) The spring constant is 1.25 N/m

c) The frequency is 1.42 Hz

d) The speed of the block is 1.08 m/s

Explanation:

We can find the mass of the block by applying the law of conservation of energy: in fact, the total mechanical energy of the system (which is sum of elastic potential energy, PE, and kinetic energy, KE) is constant:

$E=PE+KE=const.$

The potential energy is given by

$PE=\frac{1}{2}kx^2$

where k is the spring constant and x is the displacement. When the block is crossing the position of equilibrium, x = 0, so all the energy is kinetic energy:

$E=KE_{max}=\frac{1}{2}mv_{max}^2$ (1)

where

m is the mass of the block

$v_{max}=1.25 m/s$ is the maximum speed

We also know that the total energy is

$E=0.18 J$

Re-arranging eq.(1), we can find the mass:

$m=\frac{2E}{v_{max}^2}=\frac{2(0.18)}{(1.25)^2}=0.23 kg$

The maximum speed in a spring-mass system is also given by

$v_{max} =\sqrt{\frac{k}{m}} A$

where

k is the spring constant

m is the mass

A is the amplitude

Here we have:

$v_{max}=1.25 m/s$ is the maximum speed

m = 0.23 kg is the mass

A = 14.0 cm = 0.14 m is the amplitude

Solving for k, we find the spring constant

$k=\frac{v_{max}^2}{A^2}m=\frac{1.25^2}{0.14^2}(0.23)=18.3 N/m$

The frequency in a spring-mass system is given by

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

where

k is the spring constant

m is the mass

In this problem, we have:

k = 18.3 N/m is the spring constant (found in part b)

m = 0.23 kg is the mass (found in part a)

Substituting and solving for f, we find the frequency of the system:

$f=\frac{1}{2\pi}\sqrt{\frac{18.3}{0.23}}=1.42 Hz$

We can solve this part by using the law of conservation of energy; in fact, we have

$E=PE+KE=\frac{1}{2}kx^2 + \frac{1}{2}mv^2$

Where v is the speed of the system when the displacement is equal to x.

We know that the total energy of the system is

E = 0.18 J

Also we know that

k = 18.3 N/m is the spring constant

m = 0.23 kg is the mass

Substituting

x = 7.00 cm = 0.07 m

We can solve the equation to find the corresponding speed v:

$v=\sqrt{\frac{2E-kx^2}{m}}=\sqrt{\frac{2(0.18)-(18.3)(0.07)^2}{0.23}}=1.08 m/s$

#LearnwithBrainly

3 0

3 years ago

For the following statements, choose the word or words inside the parentheses that serve to make a correct statement. Each state

AnnyKZ [126]

Answer:

a) Temperatura, b) Temperature, c) Constant , d) None of these , e) Gibbs enthalpy and free energy (G)

Explanation:

a) the expression for ideal gases is PV = nRT

Temperature

b) The internal energy is E = K T

Temperature

c) S = ΔQ/T

In an isolated system ΔQ is zero, entropy is constant

Constant

d) all parameters change when changing status

None of these

e) Gibbs enthalpy and free energy

7 0

2 years ago

An electron is moving at 2.02.0 ×× 105m/s105 m/s in the positive y direction. The magnetic force on the electron is 3.03.0 ×× 10

inn [45]

Answer:

The magnitude and direction of the magnetic field is 93.63 T in negative x direction.

Explanation:

Given;

speed of the electron in positive y direction, v = 2.0 x 10⁵ m/s

magnetic force on the electron, F in negative z direction = 3.0 x 10⁻¹² N

The magnitude of the magnetic force is given by;

F = Qv x B

B = F / Qv

$B = \frac{3*10^{-12}}{ (1.602*10^{-19})(2*10^5)}\\\\B = 93.63 \ T$

The direction of the magnetic field is is as;

Based on the direction of magnetic force (negative z direction), the charge will be directed into negative y-direction because electron is negatively charged. Thus, the direction of the magnetic field will be in the negative x-direction

$F_{(-z)}= Q_{(-y)}V* B_{(-x)}$

Therefore, the magnitude and direction of the magnetic field is 93.63 T in negative x direction.

6 0

2 years ago

What is the energy equivalent of an object with a mass of 4.1 kg?

siniylev [52]

To determine the energy equivalent of an object, we use the famous equation of Einstein which is E=mc^2 where m is the mass of the object and c is the speed of light (3x10^8 m/s). We calculate as follows:

E = mc^2
E = 4.1 kg (3x10^8 m/s)^2
E = 3.69x10^17 J

6 0

3 years ago

Read 2 more answers

An infinite line of charge with charge density λ1 = 0.6 μC/cm is aligned with the y-axis.

Ganezh [65]

Answer:

1440 × 10⁴ N/C

Explanation:

Data provided in the question:

Charge density λ1 = 0.6 μC/cm = 6 × 10⁻⁵ C/m

a = 7.5 cm = 0.075 m

Now,