A solar sail is used to propel a spacecraft. It uses the pressure (force per unit area) of sunlight instead of wind. Assume the sail and its spacecraft have a mass of 245 kg. If the sail has an area of 62,500 m2 and achieves a velocity of 8.93 m/s in 12.0 hours starting from rest, what pressure does light of the Sun exert on the sail? To simplify the problem, ignore other forces acting on the spacecraft and assume the pressure is constant even as its distance from the Sun increases.

v=a•t => a=v/t,

F =m•a =>mv/t,
Pressure is
P =F/A = m•v/t•A =
245•8.93/a2•3600•62500 = 8.1•10^-7 Pa

To find the pressure exerted by sunlight on the sail, we can use the principles of momentum and force.

Step 1: Calculate the change in momentum of the spacecraft
The change in momentum (Δp) of the spacecraft is given by the formula:
Δp = m * Δv
where m is the mass of the spacecraft and Δv is the change in velocity.

Given:
Mass of the spacecraft, m = 245 kg
Change in velocity, Δv = 8.93 m/s (final velocity) - 0 m/s (initial velocity) = 8.93 m/s

Δp = 245 kg * 8.93 m/s
Δp = 2183.85 kg·m/s (rounded to two decimal places)

Step 2: Calculate the force exerted by the sunlight on the spacecraft
Force (F) can be calculated using the formula:
F = Δp / Δt
where Δt is the time interval over which the change in momentum occurs.

Given:
Time interval, Δt = 12.0 hours = 12.0 hours * 60 min/hour * 60 s/min
Δt = 43,200 s

F = 2183.85 kg·m/s / 43,200 s
F ≈ 0.0505 N (rounded to four decimal places)

Step 3: Calculate the pressure exerted by sunlight on the sail
Pressure (P) is defined as the force per unit area. The area of the sail (A) is given as 62,500 m^2.

P = F / A
P = 0.0505 N / 62,500 m^2
P = 8.08 × 10^-7 N/m^2 (rounded to three significant figures)

Therefore, the pressure exerted by sunlight on the sail is approximately 8.08 × 10^-7 N/m^2.

To find the pressure that light of the Sun exerts on the sail, we can use Newton's second law of motion and the concept of impulse.

First, let's calculate the change in momentum of the spacecraft/sail system. The change in momentum is given by the formula:

Δp = m * Δv

where Δp is the change in momentum, m is the mass of the spacecraft/sail system, and Δv is the change in velocity.

Given:
Mass of the spacecraft/sail system (m) = 245 kg
Change in velocity (Δv) = final velocity (v) - initial velocity (u)
v = 8.93 m/s (final velocity)
u = 0 m/s (initial velocity)

Δv = v - u = 8.93 m/s - 0 m/s = 8.93 m/s

Δp = 245 kg * 8.93 m/s = 2183.85 kg·m/s

Now let's calculate the impulse exerted on the spacecraft/sail system, which is equal to the change in momentum. Impulse is given by the formula:

Impulse = Force * Time

Since we are given the time (12.0 hours) and the mass (245 kg), we can rearrange the formula to solve for force:

Force = Impulse / Time

But we need to convert the time from hours to seconds. There are 3600 seconds in an hour, so:

Time = 12.0 hours * 3600 seconds/hour = 43,200 seconds

Now, substituting the values:

Force = Δp / Time = 2183.85 kg·m/s / 43,200 seconds = 0.0506 N

Finally, the pressure exerted by sunlight on the sail is force per unit area. Since pressure is force divided by the area of the sail, we can calculate it as:

Pressure = Force / Area

Given:
Area of the sail = 62,500 m^2

Pressure = 0.0506 N / 62,500 m^2 = 8.1 x 10^-7 N/m^2 (rounded to the appropriate number of significant figures)

So, the pressure that light of the Sun exerts on the sail is approximately 8.1 x 10^-7 N/m^2.