A toy plane of mass 0.624 kg is flown in a circle when attached to a string. The plane moves around the circle with a rotational speed of 8.09 rpm. The length of the string is 2.60 m.

What is the tension in the string?

tension=mass*w^2 * radius

w= 8.09 rpm*2PIrad/rev*1min/60 sec

Thanks

To determine the tension in the string, we can apply the centripetal force equation, which states that the centripetal force (Fc) acting on an object moving in a circular path is equal to the mass of the object (m) multiplied by the square of its velocity (v) divided by the radius of the circle (r).

In this case, the mass of the toy plane is given as 0.624 kg, and the rotational speed is given as 8.09 rpm. However, we need to convert the rotational speed to linear velocity to use in the equation.

To convert rpm to linear velocity, we can use the following equation:
v = 2πr(n/60), where v is the linear velocity, r is the radius, and n is the rotational speed in rpm.

Plugging in the given values, we can calculate the linear velocity:
v = 2π(2.60)(8.09/60)
v ≈ 2.704 m/s

Now that we have the linear velocity, we can calculate the tension in the string using the centripetal force equation:
Fc = m * v^2 / r

Plugging in the values we have, we get:
Fc = (0.624)(2.704^2) / 2.60
Fc ≈ 1.784 N

Therefore, the tension in the string is approximately 1.784 N.