At takeoff, a commercial jet has a 60 m/s speed. Its tires have a diameter of .850 m. With what force in N must a determined 1.00 x 10^-15 kg bacterium cling to the rim?
To find the force required for the bacterium to cling to the rim, we can calculate the centripetal force acting on it. The centripetal force can be calculated using the formula:
F = m * ω^2 * r
Where:
F is the centripetal force
m is the mass of the bacterium (1.00 x 10^-15 kg)
ω is the angular velocity (in this case, equal to the linear velocity divided by the radius)
r is the radius of the tire (diameter divided by 2)
The linear velocity can be calculated using the formula:
v = ω * r
Substituting the values given:
v = 60 m/s
r = 0.850 m / 2 = 0.425 m
Rearranging the equation to solve for ω:
ω = v / r
ω = 60 m/s / 0.425 m
ω ≈ 141.18 rad/s
Substituting the values into the centripetal force formula:
F = (1.00 x 10^-15 kg) * (141.18 rad/s)^2 * 0.425 m
F ≈ 1.00 x 10^-15 kg * 19,963.32 rad^2/s^2 * 0.425 m
F ≈ 8.51 x 10^-13 N
Therefore, the determined bacterium must cling to the rim with a force of approximately 8.51 x 10^-13 N.