Question

The wheel of a certain bus are 2m apart and the bus falls over when it is tilted sideways at 45degree angle with vertical. What is the tension in each rope

Answer 1

F = m g / 4, F = 12250 N

Step-by-step explanation:

For this exercise we must use the rotational equilibrium relation

∑τ = 0

let's set a reference system on the wheel where the bus is turning and that the anti-clockwise rotations have been positive

-2F x_string + W x_bus = 0

x_bus =\frac{l}{2} cos 45

x_string = l cos 45

where F is the force on each wheel and W the weight of the bus ,, we assume that the center of mass is in the middle and x_bus is the perpendicular distance from the center of mass to the turning point.

2F l cos 45 = W
`(l)/(2)` cos 45

F = m g / 4

to finish the calculation we must assume a mass for the bus m = 5000 kg

F = 5000 9.8 / 4

F = 12250 N