A model airplane has a mass of .90 kg and moves at a constant speed on a circle that is parallel to the ground. Find the tension in the guideline (length = 17 m) for speeds of 19 and 38 m/s.
tension=mass*v^2/r
Why did the model airplane have to join a support group? Because it was feeling a little "tens-ion" from all the pressure!
Now, let's tackle your question. To find the tension in the guideline, we'll make use of centripetal force, which is provided by tension in this case.
For a circular motion, the centripetal force is given by the equation:
F = (m * v²) / r
where:
F is the centripetal force,
m is the mass of the airplane,
v is the velocity of the airplane, and
r is the radius of the circular path.
Let's calculate the tension in the guideline for speeds of 19 m/s and 38 m/s.
First, let's calculate the centripetal force for the speed of 19 m/s:
F = (m * v²) / r
F = (0.9 kg * (19 m/s)²) / 17 m
Solving this equation will give us the value of the tension needed.
Now, let's calculate the centripetal force for the speed of 38 m/s:
F = (m * v²) / r
F = (0.9 kg * (38 m/s)²) / 17 m
Solving this equation will also give us the value of the tension required.
Remember, my jokes may be funny, but always double-check the calculations!
To find the tension in the guideline, we can use the formula for centripetal force:
F = (m * v^2) / r
where F is the centripetal force, m is the mass of the airplane, v is the speed, and r is the radius of the circle.
Given:
m = 0.90 kg
v1 = 19 m/s
v2 = 38 m/s
r = 17 m
Step 1: Calculate the tension for speed 19 m/s
F1 = (m * v1^2) / r
F1 = (0.90 kg * (19 m/s)^2) / 17 m
F1 = (0.90 kg * 361 m^2/s^2) / 17 m
F1 = 0.90 kg * 21.2353 N
F1 = 19.112 N
Therefore, the tension in the guideline for a speed of 19 m/s is approximately 19.112 N.
Step 2: Calculate the tension for speed 38 m/s
F2 = (m * v2^2) / r
F2 = (0.90 kg * (38 m/s)^2) / 17 m
F2 = (0.90 kg * 1444 m^2/s^2) / 17 m
F2 = 0.90 kg * 85.1765 N
F2 = 76.658 N
Therefore, the tension in the guideline for a speed of 38 m/s is approximately 76.658 N.
To find the tension in the guideline, we need to use the concept of centripetal force. Centripetal force is the force that keeps an object moving in a circular path and is directed towards the center of the circle.
The formula for centripetal force can be written as:
F = (m * v^2) / r
Where:
F is the centripetal force,
m is the mass of the object,
v is the velocity of the object,
and r is the radius of the circular path.
In this case, the circular path is the guideline with a length of 17 m. Since the guideline is parallel to the ground, the radius of the circular path will be half the length of the guideline, which is 8.5 m.
Now, let's calculate the tension in the guideline for speeds of 19 m/s and 38 m/s.
For a speed of 19 m/s:
F = (m * v^2) / r
F = (0.9 kg * (19 m/s)^2) / 8.5 m
F = 38.73 N
So, the tension in the guideline for a speed of 19 m/s is 38.73 N.
For a speed of 38 m/s:
F = (m * v^2) / r
F = (0.9 kg * (38 m/s)^2) / 8.5 m
F = 81.53 N
Therefore, the tension in the guideline for a speed of 38 m/s is 81.53 N.