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
change w to radians /sec
To find the tension in the string, we can use the centripetal force formula:
Fc = m * v^2 / r
Where:
Fc is the centripetal force
m is the mass of the toy plane
v is the velocity of the toy plane
r is the radius of the circular path
First, let's convert the rotational speed from RPM to rad/s:
ω = 2π * f
Where:
ω is the angular velocity in rad/s
f is the frequency in Hz (rotations per second)
Given:
f = 8.09 rpm
r = 2.60 m
m = 0.624 kg
First, let's convert the rotational speed from RPM to rad/s:
ω = 2π * f
Plugging in the given values:
ω = 2π * 8.09 rpm
ω = 2π * (8.09 / 60) Hz
ω ≈ 0.847 rad/s
Now, let's calculate the centripetal force using the formula:
Fc = m * ω^2 / r
Plugging in the given values:
Fc = 0.624 kg * (0.847 rad/s)^2 / 2.60 m
Fc ≈ 0.181 N
Therefore, the tension in the string would be approximately 0.181 N.