Question: The model airplane in the figure below has a mass of 0.80 kg and moves at a constant speed on a circle that is parallel to the ground. Assume that there is no upward lift on the plane generated by its wings. Without such lift, the guideline slopes downward due to the weight of the plane. Find the tension T in the guideline (length = 18 m), for purposes of significant figures, use 0.800 kg for the mass of the plane, 18.0 m for the length of the guideline, and s1 = 18.0 and s2 = 41.0 m/s for the speeds.
This is a practice question and the answers are given.
Tension for s1: 17.8 N
Tension for s2: 75.5 N
To find the tension in the guideline for the given scenarios, we can make use of the centripetal force formula:
F = (m * v^2) / r
where F is the centripetal force, m is the mass of the object, v is its velocity, and r is the radius of the circular path.
In this case, the tension in the guideline is equal to the centripetal force acting on the plane.
For scenario 1 (s1 = 18.0 m/s):
We are given:
- Mass of the plane (m) = 0.800 kg
- Speed of the plane (v) = 18.0 m/s
- Length of the guideline (r) = 18.0 m
Using the formula, we can calculate the tension:
T1 = (m * v^2) / r
= (0.800 kg * (18.0 m/s)^2) / 18.0 m
= 17.8 N (rounded to one decimal place)
Therefore, the tension in the guideline for scenario 1 is 17.8 N.
For scenario 2 (s2 = 41.0 m/s):
We are given:
- Mass of the plane (m) = 0.800 kg
- Speed of the plane (v) = 41.0 m/s
- Length of the guideline (r) = 18.0 m
Using the same formula, we can calculate the tension:
T2 = (m * v^2) / r
= (0.800 kg * (41.0 m/s)^2) / 18.0 m
= 75.5 N (rounded to one decimal place)
Therefore, the tension in the guideline for scenario 2 is 75.5 N.
To summarize:
- Tension for scenario 1 (s1 = 18.0 m/s): 17.8 N
- Tension for scenario 2 (s2 = 41.0 m/s): 75.5 N