A 8.0×10−2- toy airplane is tied to the ceiling with a string. When the airplane's motor is started, it moves with a constant speed of 1.30 in a horizontal circle of radius 0.49 , as illustrated in the figure .

Find the angle the string makes with the vertical.

Find the tension in the string.

Anyone know how to solve this problem?

retrd

To find the angle the string makes with the vertical, we can consider the forces acting on the toy airplane. In this case, there are two forces at play: the tension in the string and the gravitational force.

1. Angle with the Vertical:
Let's consider a free body diagram of the toy airplane at the topmost point of its circular motion. At this point, the gravitational force and the tension in the string are acting on the airplane.

The gravitational force acts vertically downward, while the tension in the string acts along the string. Since the toy airplane is moving in a horizontal circular motion, the net force acting on it must be pointing towards the center of the circle. The vertical component of the tension must balance out the gravitational force.

Now, we can divide the forces into their respective components:
- Gravitational force = m * g (mass * acceleration due to gravity), acting vertically downward.
- Tension in the string can be divided into horizontal and vertical components: T_x and T_y.

Since the net force is pointing towards the center of the circle:
F_net = T_x = m * (v^2 / r)

From the right triangle formed by T_y, T_x, and Tension:
T_y = Tension * cos(angle)

Since T_y balances the gravitational force in the vertical direction, we have:
T_y = m * g

From here, we can equate the two expressions for T_y:
Tension * cos(angle) = m * g
cos(angle) = (m * g) / Tension
angle = arccos((m * g) / Tension)

Now, we can substitute the given values in the equation to calculate the angle the string makes with the vertical.

2. Tension in the string:
To find the tension in the string, we need to consider the horizontal component of the tension (T_x), as this force is providing the centripetal force required for the circular motion.

T_x = m * (v^2 / r)

Again, we need to substitute the given values in the equation to calculate the tension in the string.

Note: Make sure to convert all values to SI units (kilograms, meters, and seconds) before substituting them into the equations.