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.
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?
1 answer