Question

The model airplanc has a mass of 3 kg, and is flying horizontally at a

constant speed of 21 m/s at a radius of 2.7 m.
a) What tension is in the string?
b) If the plane's mass is doubled, what happens to the tension is part a?
c) If the plane's speed is doubled, what happens to the tension is part a?
d) If the string's length is doubled, what happens to the tension is part a?

Answer 1

The tension in the string can be found using the formula for centripetal force. If the mass, speed, or length of the string changes, the tension will change accordingly.

Step-by-step explanation:

To find the tension in the string, we can use centripetal force. The centripetal force acting on the airplane is provided by the tension in the string. The formula for centripetal force is Fc = (mv^2) / r, where Fc 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.

Using the given values, we can substitute them into the formula: Fc = (3 kg)(21 m/s)^2 / 2.7 m = 220.22 N

So, the tension in the string is approximately 220.22 N.

b) If the mass of the airplane is doubled, the centripetal force will also double, resulting in a doubled tension in the string.

c) If the speed of the airplane is doubled, the centripetal force will quadruple (since centripetal force is proportional to the square of the velocity), resulting in a quadrupled tension in the string.

d) If the length of the string is doubled, the centripetal force will be halved (since the radius is doubled), resulting in a halved tension in the string.