A person is flying a model airplane with mass 82.2 gram in a horizontal circular path on the

end of a string 10.5 m long. The string is horizontal and exerts a force of 3.22 N on the hand
of the person holding it. What is the speed (in m/s) of the plane?

PLEASE LEAVE FULL ANSWERS

Centripetal force is the force that maintains an object in a circular motion. This is an external force that acts on the object in the direction of the centre of the circular motion, namely tension of the string in this case.

Centripetal force may be calculated using the formula:
F = mv²/r
m=mass (kg)
v=tangential velocity (m/s)
r=radius (m)

To find the speed of the model airplane, we need to first determine the tension in the string. The tension in the string is equal to the centripetal force acting on the airplane.

Step 1: Determine the centripetal force:
The centripetal force (Fcp) is given by the equation:

Fcp = (m * v^2) / r

where,
m = mass of the object (82.2 grams = 0.0822 kg)
v = velocity of the object (speed of the airplane)
r = radius of the circular path (length of the string = 10.5 m)

Step 2: Convert mass to kilograms:
Since the mass is given in grams, we need to convert it to kilograms:
m = 0.0822 kg

Step 3: Rearrange the equation:
Rearranging the equation, we can solve for the speed (v):

v^2 = (Fcp * r) / m

Step 4: Substitute the given values:
Substituting the known values into the equation, we have:

v^2 = (3.22 N * 10.5 m) / 0.0822 kg

Step 5: Calculate the speed (v):
Now we can calculate the speed by taking the square root of both sides of the equation:

v = √((3.22 N * 10.5 m) / 0.0822 kg)

Calculating this expression will give us the speed of the model airplane in meters per second.

To find the speed of the model airplane, we need to consider the forces acting on it and apply the principles of circular motion.

In this scenario, the force acting on the model airplane is the tension in the string, which is directed towards the center of the circular path. This force provides the necessary centripetal force to keep the plane moving in a circle.

First, let's convert the mass of the airplane to kilograms:
Mass = 82.2 grams = 0.0822 kg

Next, we need to determine the net force acting on the airplane. The only force acting horizontally is the tension in the string, which is given as 3.22 N.

Since the net force acting on an object moving in a circle is given by:
Net Force = (mass * velocity^2) / radius

In this case, the net force is equal to the tension in the string:
Tension = (mass * velocity^2) / radius

We know the mass (0.0822 kg) and the radius (10.5 m), and we need to solve for velocity.

Rearranging the formula, we get:
velocity^2 = (Tension * radius) / mass

Plugging in the known values, we have:
velocity^2 = (3.22 N * 10.5 m) / 0.0822 kg

Simplifying the equation, we find:
velocity^2 = 415.95 m^2/s^2

To solve for velocity, we take the square root of both sides:
velocity = √(415.95 m^2/s^2)

Evaluating this expression gives us the speed of the model airplane:
velocity ≈ 20.4 m/s

Therefore, the speed of the model airplane is approximately 20.4 m/s.