Question

[Warning Physics involved] The school bus with a total mass of 10 tonnes travels at a constant velocity of 40km/h down a long hill with a slope of 15 degrees. determine the braking force required to stop the bus within 50 metres from where the driver applies the brakes.

Answer 1

From kinematics we need to determine the deceleration required to bring the object to rest in 50 meters. This is expressed as\[V_f^2 = V_o^2 + 2 a_b(\Delta X)\]

From kinetics, we can determine the braking force required to produce the necessary deceleration. From Newton's First Law, \[\sum F = ma\]Summing the forces along the direction of travel yields, \[m*g*\sin(15^\circ) - F_b = m*a_b\]This can readily be solved for \(F_b\).