Question

A bus of mass 7.5 tonnes has a velocity of 72 km/h when the brakes are applied. The force of the braking system can be considered to be a constant 25 kN and is applied for 40 m. Determine the final velocity of the lorry in m/s.

Answer 1

Answer on Question #44567, Physics, Mechanics | Kinematics | Dynamics

Question:

A bus of mass 7.5 tonnes has a velocity of $72\,\mathrm{km/h}$ when the brakes are applied. The force of the braking system can be considered to be a constant $25\,\mathrm{kN}$ and is applied for $40\,\mathrm{m}$. Determine the final velocity of the lorry in $\mathrm{m/s}$.

Answer:

The law of conservation of energy:

$$\Delta E = W$$

where $\Delta E$ – change of body’s energy, $W$ – work of all forces acting on the body

Work can be expressed by the following equation:

$$W = F d \cos \theta$$

where $F$ is the force, $d$ is the displacement, and the angle $\theta$ is defined as the angle between the force and the displacement vector.

Work of brakes equals:

$$W = F \cdot d \cos 180{}^\circ = -F d$$

Change of body’s kinetic energy equals:

$$\Delta E = \frac{m v^2}{2} - \frac{m v_0^2}{2}$$

where $v$ is final velocity, $v_0$ is initial.

Therefore:

$$\frac{m v^2}{2} - \frac{m v_0^2}{2} = -F d$$ $$v = \sqrt{v_0^2 - \frac{2 F d}{m}} = \sqrt{\left(\frac{72\,\mathrm{m}}{\mathrm{s}}\right)^2 - \frac{2 \cdot 25\,\mathrm{kN} \cdot 40\,\mathrm{m}}{7500\,\mathrm{kg}}} \cong 12\,\frac{\mathrm{m}}{\mathrm{s}}$$

Answer: $12\,\frac{\mathrm{m}}{\mathrm{s}}$

http://www.AssignmentExpert.com/