All categories

2 years ago

Consider and mass of a material

1 answer:

3 0

Answer:Density is the mass of an object divided by its volume. Density often has units of grams per cubic centimeter (g/cm3). ... You probably have an intuitive feeling for density in the materials you use often. For example, sponges are low in density; they have a low mass per unit volume.

Explanation:

You might be interested in

Assume that a pendulum used to drive a grandfather clock has a length L0=1.00m and a mass M at temperature T=20.00°C. It can be

Sedaia [141]

Answer:

The period will change a 0,036 % relative to its initial state

Explanation:

When the rod expands by heat its moment of inertia increases, but since there was no applied rotational force to the pendulum , the angular momentum remains constant. In other words:

ζ= Δ(Iω)/Δt, where ζ is the applied torque, I is moment of inertia, ω is angular velocity and t is time.

since there was no torque ( no rotational force applied)

ζ=0 → Δ(Iω)=0 → I₂ω₂ -I₁ω₁ = 0 → I₁ω₁ = I₂ω₂

thus

I₂/I₁ =ω₁/ω₂ , (2) represents final state and (1) initial state

we know also that ω=2π/T , where T is the period of the pendulum

I₂/I₁ =ω₁/ω₂ = (2π/T₁)/(2π/T₂)= T₂/T₁

Therefore to calculate the change in the period we have to calculate the moments of inertia. Looking at tables, can be found that the moment of inertia of a rod that rotates around an end is

I = 1/3 ML²

Therefore since the mass M is the same before and after the expansion

I₁ = 1/3 ML₁² , I₂ = 1/3 ML₂² → I₂/I₁ = (1/3 ML₂²)/(1/3 ML₁²)= L₂²/L₁²= (L₂/L₁)²

since

L₂= L₁ (1+αΔT) , L₂/L₁=1+αΔT , where ΔT is the change in temperature

now putting all together

T₂/T₁=I₂/I₁=(L₂/L₁)² = (1+αΔT) ²

finally

%change in period =(T₂-T₁)/T₁ = T₂/T₁ - 1 = (1+αΔT) ² -1

%change in period =(1+αΔT) ² -1 =[ 1+18×10⁻⁶ °C⁻¹ *10 °C]² -1 = 3,6 ×10⁻⁴ = 3,6 ×10⁻² % = 0,036 %

4 0

3 years ago

Envision holding the end of a ruler with one hand and deforming it with the other. When you let go, you can see the oscillations

lapo4ka [179]

Answer: To increase the rigidity of the system you could hold the ruler at its midpoint so that the part of the ruler that oscillates is half as long as in the original experiment.

Explanation:

When a rule is displaced from its vertical position, it oscillates back and forth because of the restoring force opposing the displacement. That is, when the rule is on the left there is a force to the right.

By holding a ruler with one hand and deforming it with the other a force is generated in the opposite direction which is known as the restoring force. The restoring force causes the ruler to move back toward its stable equilibrium position, where the net force on it is zero. The momentum gained causes the ruler to move to the right leading to opposite deformation. This moves the ruler again to the left. The whole process is repeated until dissipative forces reduce the motion causing the ruler to come to rest.

The relationship between restoring force and displacement was described by Hooke's law. This states that displacement or deformation is directly proportional to the deforming force applied.

F= -kx, where,

F= restoring force

x= displacement or deformation

k= constant related to the rigidity of the system.

Therefore, the larger the force constant, the greater the restoring force, and the stiffer the system.

5 0

2 years ago

A sinusoidal wave has the following wave function: y(x,t) = (2.5 m) sin((3.0 m ) x - (24 s-')t + Tt/2] What is the frequency of

vladimir1956 [14]

Answer:

Frequency of the wave is 3.8 hertz.

Explanation:

It is given that, the sinusoidal wave has following wave equation as :

$y(x,t)=(2.5\ m)sin[(3\ m^{-1})x-(24\ s^{-1})t+\pi/2]$

The general equation for the sinusoidal wave is :

$y=A\ sin(kx-\omega t+\phi)$

Where

A is the amplitude

k is the constant

$\omega$ is the angular frequency

$\phi$ is the phase difference

Since, $\omega=24\ s^{-1}$

$2\pi f=24$

$f=\dfrac{24}{2\pi}=3.81\ Hz$

f = 3.8 Hz

So, the frequency of the wave is 3.8 hertz. Hence, this is the required solution.

8 0

2 years ago

A person walks due south from point A for 500 yards and then due west for 300 yards, arriving at point B. Answer the following q

Pepsi [2]

The total displacement of the person walking from point A to point B is 300 yards.

As shown in the figure we can conclude that the required method to calculate the total displacement is the Pythagoras theorem.

<h3>Pythagoras theorem in brief :</h3>

According to the Pythagorean Theorem, the square that represents the hypotenuse, or side of a right triangle that faces the right angle, is equal to the total of the squares on the triangle's legs.(or, in popular algebraic notation, $a^2 + b^2 = c^2$ ).