A weather balloon travels upward for 6 km whi le the wind blows it 10 km north and 8 km east. Approximately what is its final di

Response:

Explanation:

Let T denote the tension.

By employing Newton's second law to analyze the bucket's downward motion, we have:

mg - T = ma

A torque, TR, acts on the drum, inducing an angular acceleration α in it. If I refers to the moment of inertia of the drum, then:

TR = Iα

Rearranging gives: TR = Ia/R

This leads to T =  Ia/R²

Substituting this expression for T back into the previous equation yields:

mg - T = ma

mg - Ia/R² = ma

Consequently, we find that mg =  Ia/R² + ma

Therefore, a (I/R² + m) = mg

This results in: a = mg / (I/R² + m)

Next, we aim to express T as:

mg - T = ma

which simplifies to mg - ma  = T

Rearranging gives mg - m²g / (I/R² + m) = T

Thus, we arrive at: mg - mg / (1 + I / m R²) = T

For part (b), T =  Ia/R²

and for part (c), the moment of inertia of a hollow cylinder calculates to:

I = 1/2  M (R² - (R² / 4))

This simplifies to 3/4 x 1/2 MR², yielding 3/8 MR²

Thus, I / R² = 3/8 M

When we substitute, we find a = mg / (3/8 M + m)

and subsequently T =  Ia/R²

= 3/8 MR² × mg / (3/8 M + m) × 1/R²

Results in:

The response is outlined below. Audio power amplifiers are present in various sound systems, including those for sound reinforcement, public addresses, home audio, and musical instrument amplifiers like those for guitars. This component is the final electronic element in the audio playback chain before signals reach the loudspeaker. To achieve the loudest possible sound, it is essential to maximize output while maintaining high input and low output impedance.

Since there is no friction in the bowl, the total mechanical energy remains constant. Thus, we can conclude that the initial potential energy of the butter is equal to its final kinetic energy at the bowl's bottom, allowing us to calculate the speed v.

To find the time required for one revolution, compute as follows:
0.510 s / 440 revolutions = 51/44000 s
. The frequency in Hertz is the reciprocal of this figure, resulting in a frequency of about 862.75 Hz.
The angular velocity in radians per second
is calculated as (440 rev / 0.510 s) x (2π rad / 1 rev) = 5420.787 rad/s
. The period, which is the inverse of frequency, is approximately equal to 1.16x10^-3 s.

Transverse waves propagate in a direction that is at right angles to the movement of the particles (or the medium involved). Hence, the particles would be shifting from east to west, which is perpendicular to the north-south direction of the wave.