A factor that determines the inertia of an object is

when a circular plate of metal is heated in an oven, its radius increases at .03 cm/min, at what rate is the area increasing whe

Alinara [238K]

Answer:

Rate of change of area will be $9.796cm^2/min$

Explanation:

We have given rate of change of radius $\frac{dr}{dt}=0.03cm/min$

Radius of the circular plate r = 52 cm

Area is given by $A=\pi r^2$

So $\frac{dA}{dt}=2\pi r\frac{dr}{dt}$

Puting the value of r and $\frac{dr}{dt}$

$\frac{dA}{dt}=2\times 3.14\times 52\times 0.03=9.796cm^2/min$

So rate of change of area will be $9.796cm^2/min$

6 0

3 years ago

A mass free to vibrate on a level, frictionless surface at the end of a horizontal spring is pulled 35 cm from its equilibrium p

saul85 [17]

Answer:

0.67 s

Explanation:

This is a simple harmonic motion (SHM).

The displacement, $x$ , of an SHM is given by

$x = A\cos(\omega t)$

A is the amplitude and $\omega$ is the angular frequency.

We could use a sine function, in which case we will include a phase angle, to indicate that the oscillation began from a non-equilibrium point. We are using the cosine function for this particular case because the oscillation began from an extreme end, which is one-quarter of a single oscillation, when measured from the equilibrium point. One-quarter of an oscillation corresponds to a phase angle of 90° or $\frac{\pi}{4}$ radian.

From trigonometry, $\sin A =\cos B$ if A and B are complementary.

At $t = 0$ , $x = 3.5$

$3.5 = A\cos(\omega \times0)$

$A =3.5$

So

$x = 3.5\cos(\omega t)$

At $t = 0.12$ , $x = 1.5$

$1.5 = 3.5\cos(0.12\omega)$

$\cos(0.12\omega)=\dfrac{1.5}{3.5}=0.4286$

$0.12\omega =\cos^{-1}0.4286$

$0.12\omega = 1.13$

$\omega = 9.4$

The period, $T$ , is related to $\omega$ by

$T = \dfrac{2\pi}{\omega} = \dfrac{2\times3.14}{9.4}=0.67$

5 0

3 years ago

The fourth harmonic on a string fixed at both ends shows

Charra [1.4K]

Answer:

I believe the answer is B) Two wavelengths

8 0

3 years ago

An RLC circuit is used in a radio to tune into the radio lagos fm Station broadcasting at 93.5Hz. The resistance is 15ohms and t

bazaltina [42]

The characteristics of the RLC circuit allow to find the result for the capacitance at a resonance of 93.5 Hz is:

Capacitance is C = 1.8 10⁻⁶ F

A series RLC circuit reaches the maximum signal for a specific frequency, called the resonance frequency, this value depends on the impedance of the circuit.

$Z^2 = R^2 + ( wL - \frac{1}{wC} )^2$

Where Z is the impedance of the circuit, R the resistance, L the inductance, C the capacitance and w the angular velocity. The negative sign is due to the fact that the current in the capacitor and the inductor are out of phase.

In the case of resonance, the impedance term completes the circuit as a resistive system.

$wL - \frac{1}{wC} = 0 \\w^2 = \frac{1}{LC}$

Indicate that the inductance L = 1.6 H and the frequency f = 93.5 Hz.

Angular velocity and frequency are related.

w = 2π f

Let's substitute.

$C = \frac{1}{L ( 2 \pi f)^2 }$

Let's calculate.

$C = \frac{1}{1.6 \ ( 2\pi \ 93.5)^2}$

C = 1.8 10⁻⁶ F

In conclusion with the characteristics of the RLC circuits we can find the result for the capacitance at a 93.5 Hz resonance is:

Capacitance is C = 1.8 10⁻⁶ F

Learn more about serial RLC circuits here: brainly.com/question/15595203

4 0

2 years ago

Sound waves strike a glass and cause it to shatter.

e-lub [12.9K]

1. Resonance. Mechanical waves act on or through a medium, these waves can often have frequencies that are synchronized in a way that makes them act on the matter in the medium more "aggressively."

3 0

3 years ago