Question

A man seeking to set a world record wants to tow a 101,000-kg airplane along a runway by pulling horizontally on a cable attached to the airplane. The mass of the man is 84 kg, and the coefficient of static friction between his shoes and the runway is 0.76. What is the greatest acceleration the man can give the airplane? Assume that the airplane is on wheels that turn without any frictional resistance.

Answer 1

6.19 x
`10^(-3)` m/
`s^(2)`

Step-by-step explanation:

For this exercise we need to sum the forces on the y-axis and x-axis as follows:

∑
`F_(y)` = N - mg = m.
`a_(y)` = 0

From the exercise, we deduce there is no motion in y-axis, so:

N = mg

Then for x-axis we have:

∑
`F_(x)` = H -
`f^(s)` = m.
`a_(x)` = 0

Now, from the exercise we deduce that we are looking for the greatest static friction which means to have the maximun static friction to start moving, so at this point the acceleration is zero, so we can find horizontal force (H), which then will act in the airplane to move it. Therefore we have:

H =
`f^(s)` =
`f^{sma_(x) }` =
`u_(s)`N =
`u_(s)`mg

H = (0.76)(84Kg)(9.8m/
`s^(2)`)

H = 625.63 N

Now we apply this force to the weight of the plane to find the greatest acceleration the mann can give to start moving the plane.

a =
`(F)/(m)` =
`(H)/(m)`

a =
`(6325.63N)/(101000Kg)`

a = 6.19 x
`10^(-3)` m/
`s^(2)`