Question : When the driver applies the brakes of a light truck travelin...

Engineering Mechanics: Dynamics-Solution Manual [EXP-760]

When the driver applies the brakes of a light truck traveling 40 km/h, it skids 3 m before stopping. How far will the truck skid if it is traveling 80 km/h when the brakes are applied?

Question Data is a breakdown of the data given in the question above.

Initial speed: 40 km/h
Initial skid distance: 3 m
Final speed: 80 km/h

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Step 1:

Convert the initial speed from km/h to m/s. Given that the light truck is traveling at 40 km/h, we need to convert this to m/s. You can do this by dividing the speed in km/h by 3.6. In this case, the initial speed is 40 km/h, so by dividing it by 3.6, we get the initial speed in m/s as 11.11 m/s.

Step 2:

Calculate the coefficient of kinetic friction. To solve the problem, we need to find the coefficient of kinetic friction. We can use the equation T1 + ΣU1-2 = T2, where T1 represents the kinetic energy at the beginning, ΣU1-2 represents the work done by friction, and T2 represents the kinetic energy at the end.

Step 3:

Calculate the work done by friction. To calculate the work done by friction, we can use the equation ΣU1-2 = μk mg d, where μk represents the coefficient of kinetic friction, m represents the mass of the truck, g represents the acceleration due to gravity, and d represents the distance over which the truck skids. Given that the truck skids 3 m before stopping, we can substitute the values into the equation: ΣU1-2 = μk mg 3.

Step 4:

Calculate the coefficient of kinetic friction. Using the equation from Step 2, T1 + ΣU1-2 = T2, we can substitute the values to solve for the coefficient of kinetic friction. T1 is equal to 1/2 m (initial speed)^2, T2 is equal to 1/2 m (final speed)^2, and ΣU1-2 is equal to μk mg d.

Step 5:

Convert the final speed from km/h to m/s. Similarly to Step 1, we need to convert the final speed of the truck from km/h to m/s. The given final speed is 80 km/h, so by dividing it by 3.6, we get the final speed in m/s as 22.22 m/s.

Step 6:

Solve for the distance the truck will skid. Using the equation from Step 4, T1 + ΣU1-2 = T2, we can substitute the values to solve for the distance the truck will skid. T1 is equal to 1/2 m (initial speed)^2, T2 is equal to 1/2 m (final speed)^2, ΣU1-2 is equal to μk mg d, and we need to solve for d.

Step 7:

Calculate the distance the truck will skid. By substituting the known values into the equation from Step 6, we can solve for the distance the truck will skid. This will give us the final answer to the problem.

Final Answer

40km/h=\frac { 40({ 10 }^{ 3 }) }{ 3600 } =11.11m/s\quad \quad 80km/h=22.22m/s\\ { T }_{ 1 }+\Sigma { U }_{ 1-2 }={ T }_{ 2 }\\ \frac { 1 }{ 2 } m{ (11.11) }^{ 2 }-{ \mu }_{ k }mg(3)=0\\ { \mu }_{ k }g=20.576\\ { T }_{ 1 }+\Sigma { U }_{ 1-2 }={ T }_{ 2 }\\ \frac { 1 }{ 2 } m({ 22.22) }^{ 2 }-(20.576)m(d)=0\\ d=12m