A hot air balloon of total mass M (including passengers and luggage) is moving with a downward acceleration of magnitude a. As i

First, we must transform the pressure into SI units, considering that :


The starting and ending volumes of the gas will be as follows (keeping in mind that ):



Thus, the work performed on the gas by its surroundings is

The positive outcome indicates that this work leads to a rise in the gas's internal energy.

When air is forced into the open pipe,

L =

where n represents any whole number such as 1,2,3,4, etc., and λ denotes the wavelength of the oscillation

This implies λ=

It is important to note that n=1 corresponds to the fundamental frequency, n=2 corresponds to the first harmonic, and so forth.

Thus, the third harmonic will be for n=4

With L=6m and n=4, solving for λ yields:

λ= =3m

The connection between frequency (f), sound speed (c), and wavelength (λ) is given by:

c=f.λ or f=

Therefore, f=

≈115 Hz

The required lift force is approximately 866.92 N. To determine this, we first establish the shark's mass at 92 kg and its density at 1040 kg/m³. The volume of the shark is calculated by dividing mass by density, yielding 0.08846 m³. The buoyant force acting on the shark is then determined by multiplying the volume by the density of water and gravity, resulting in a lift force of 866.92 N.

Answer:

1.5 m/s²

Explanation:

Begin by sketching a free body diagram.  Three forces are at play on the sea lion: the force of gravity acting downwards, the normal force that is perpendicular to the ramp, and the frictional force parallel to the ramp.

Considering the forces perpendicular to the incline:

∑F = ma

N − mg cos θ = 0

This gives us N = mg cos θ

Next, examining the forces parallel to the incline:

∑F = ma

mg sin θ − Nμ = ma

Substituting for N yields:

mg sin θ − (mg cos θ) μ = ma

g sin θ − g cos θ μ = a

hence a = g (sin θ − μ cos θ)

If we set θ = 23° and μ = 0.26:

a = 9.8 (sin 23 − 0.26 cos 23)

this results in a = 1.48

When rounded to two significant figures, the acceleration of the sea lion is 1.5 m/s².

(B) (length)/(time³) Explanation: The term x = ½ at² + bt³ should meet dimensional consistency. This means that both bt³ and ½ at² must share the same units, which are length. To find the dimension of b, we rearrange the equation: [x] = [b]*[t]³ leads to length = [b]*time³, hence [b] = length/time³.