A car drives at 15 m/s and has an air resistance force of 277 N. What is the air resistance force at 30 m/s?
A truck drives at 9.7 m/s and has an air resistance force of 380 N. What is the air resistance force at 32 m/s?
A 85.0 kg skydiver is falling at a constant speed of 32.8 m/s. What is his air resistance force?
His friend has an identical parachute, but falls at a constant 40.2 m/s. What is the friend's mass?
generally, air resistance drag is proportional to the square of velocity.
a. double speed, air resistance goes up by two squared, or 4*277N
b. speed up by 32/9.7 (3.3), so resittance goes up be a factor 0f 3.3^2
c. constant speed, then air resistance equals mg..
speed up up by (40.2/32.8) so resistance is now (40.2/32.8)^2 * 85*g, which is the weight of the friend
Why did the car join the circus? Because it wanted to be a drag performer! Okay, let's calculate the air resistance forces.
For the first question:
At 15 m/s, the car has an air resistance force of 277 N. If we assume that the air resistance force is directly proportional to the speed squared, we can use that to find the air resistance force at 30 m/s.
(30 m/s / 15 m/s)^2 = 4
So, at 30 m/s, the air resistance force would be 4 times the original force.
277 N * 4 = 1108 N
Therefore, the air resistance force at 30 m/s would be 1108 N.
For the second question:
Using the same logic, we can find the air resistance force at 32 m/s.
(32 m/s / 9.7 m/s)^2 ≈ 10.98
So, at 32 m/s, the air resistance force would be approximately 10.98 times the original force.
380 N * 10.98 ≈ 4174.4 N
Therefore, the air resistance force at 32 m/s would be approximately 4174.4 N.
Now, let's move on to the skydiver.
We can assume that the air resistance force is equal to the weight of the skydiver since the terminal velocity is constant.
Using the formula F = mg, where m is the mass of the skydiver and g is the acceleration due to gravity (approximately 9.8 m/s^2), we can find the air resistance force.
F = 85.0 kg * 9.8 m/s^2 = 833 N
Therefore, the air resistance force on the skydiver would be 833 N.
Finally, for the friend's mass:
Since the friend falls at a constant speed of 40.2 m/s and has an identical parachute, we can use the same air resistance force as the skydiver.
833 N = m * 9.8 m/s^2
Solving for m:
m ≈ 85.0 kg
Therefore, the friend's mass would be approximately 85.0 kg.
I hope this helps, and remember to always keep it light-hearted!
To calculate the air resistance force at different speeds, we can use the equation for air resistance force:
F = 1/2 * p * A * Cd * v^2
Where:
F is the air resistance force
p is the density of air (approximately 1.2 kg/m^3)
A is the cross-sectional area of the object
Cd is the drag coefficient of the object
v is the velocity of the object
Let's calculate the air resistance forces step by step.
1. Car at 15 m/s:
Given:
v = 15 m/s
F = 277 N
Using the equation F = 1/2 * p * A * Cd * v^2, we can solve for A * Cd:
A * Cd = 2 * F / (p * v^2)
A * Cd = 2 * 277 N / (1.2 kg/m^3 * (15 m/s)^2)
A * Cd ≈ 0.3851 m^2
2. Car at 30 m/s:
Given:
v = 30 m/s
Using the calculated value of A * Cd from the previous step, we can calculate the air resistance force:
F = 1/2 * p * A * Cd * v^2
F = 1/2 * 1.2 kg/m^3 * 0.3851 m^2 * (30 m/s)^2
F ≈ 2316.6 N
Therefore, the air resistance force at 30 m/s is approximately 2316.6 N.
3. Truck at 9.7 m/s:
Given:
v = 9.7 m/s
F = 380 N
Using the equation F = 1/2 * p * A * Cd * v^2, we can solve for A * Cd:
A * Cd = 2 * F / (p * v^2)
A * Cd = 2 * 380 N / (1.2 kg/m^3 * (9.7 m/s)^2)
A * Cd ≈ 0.6905 m^2
4. Truck at 32 m/s:
Given:
v = 32 m/s
Using the calculated value of A * Cd from the previous step, we can calculate the air resistance force:
F = 1/2 * p * A * Cd * v^2
F = 1/2 * 1.2 kg/m^3 * 0.6905 m^2 * (32 m/s)^2
F ≈ 2202.0 N
Therefore, the air resistance force at 32 m/s is approximately 2202.0 N.
5. Skydiver falling at 32.8 m/s:
Given:
v = 32.8 m/s
Using the equation F = 1/2 * p * A * Cd * v^2, we can solve for A * Cd:
A * Cd = 2 * F / (p * v^2)
A * Cd = 2 * F / (1.2 kg/m^3 * (32.8 m/s)^2)
A * Cd ≈ 0.6418 m^2
Now, let's calculate the air resistance force for the skydiver:
F = 1/2 * p * A * Cd * v^2
F = 1/2 * 1.2 kg/m^3 * 0.6418 m^2 * (32.8 m/s)^2
F ≈ 253.1 N
Therefore, the air resistance force for the skydiver is approximately 253.1 N.
6. Friend's mass:
Given:
v = 40.2 m/s
F = 253.1 N
Using the equation F = 1/2 * p * A * Cd * v^2, we can solve for A * Cd:
A * Cd = 2 * F / (p * v^2)
A * Cd = 2 * 253.1 N / (1.2 kg/m^3 * (40.2 m/s)^2)
A * Cd ≈ 0.2268 m^2
Now, let's calculate the mass of the friend:
Mass = F / (g * A * Cd)
Mass = 253.1 N / (9.8 m/s^2 * 0.2268 m^2)
Mass ≈ 11.0 kg
Therefore, the friend's mass is approximately 11.0 kg.
To solve these questions, we can use the formula for air resistance force:
Air resistance force (F) = 0.5 * coefficient of air resistance (C) * density of air (p) * velocity of the object squared (v^2)
Now we need to determine the missing variables in each question.
1) Car driving at 15 m/s with an air resistance force of 277 N. We need to find the air resistance force when it is driving at 30 m/s.
We already know the initial velocity (15 m/s), the air resistance force (277 N), and the new velocity (30 m/s). We can use these values to find the missing variable - the coefficient of air resistance (C).
2) Truck driving at 9.7 m/s with an air resistance force of 380 N. We need to find the air resistance force when it is driving at 32 m/s.
Similar to the previous question, we know the initial velocity (9.7 m/s), the air resistance force (380 N), and the new velocity (32 m/s). We can use these values to find the missing variable - the coefficient of air resistance (C).
3) Skydiver with a mass of 85.0 kg falling at a constant speed of 32.8 m/s. We need to find the air resistance force.
In this question, we have the mass (85.0 kg), the velocity (32.8 m/s), and need to find the air resistance force (F). We can use the formula mentioned earlier to calculate it.
4) Friend with an identical parachute falling at a constant 40.2 m/s. We need to find the friend's mass.
In this question, we have the velocity (40.2 m/s), and need to find the mass. We can use the formula mentioned earlier to calculate it, but we'll need additional information - the coefficient of air resistance (C), which we don't have in this question.
To summarize, we can solve these questions using the formula for air resistance force, but we'll need different pieces of information in each question.