Vehicle Around a Curve#

To ensure that motorists stay on roads with tight turns, it is common to tild (or bank) the roads toward the centre of the turn. A semi-truck going around a banked curve without sliding is shown on the left of the figure below and its corresponding free body diagram is shown on the right of the figure below. In the free body diagram \(\vec{W}_{\textit{E on v}}\) is the weight of the semi-truck, \(\vec{n}_{\textit{r on v}}\) is the normal force of the road on the semi-truck, and \(\vec{F}\_{\textit{net on v}}\) is the net force on the semi-truck. Take the angle to be \(\theta = {{ params.ang }}^\circ\) and the radius of curvature (distance from the centre of the circle to the semi-truck) to be \(r = {{ params.rad }}\) \(\rm{m}\).

On the left is an image showing a vehicle on a banked curved road. The image shows the back of the vehicle and a cross section of the banked road. The road is banked to the right and makes an angle of theta with the horizontal. On the right is an image of the free body diagram associated with the vehicle on the banked curved road. The normal force of the road on the vehicle makes an angle of theta with the positive y-axis and lies between the positive y-axis and the positive x-axis. The weight of the vehicle is along the negative y-axis. The net force on the vehicle is along the positive x-axis.

Part 1#

Write the equation for Newton’s second law in the \(x\)-direction.

Note that it may not be necessary to use every variable. Use the following table as a reference for each variable:

For

Use

\(W\_{\textit{E on v}}\)

W

\(n\_{\textit{r on v}}\)

n

\(\theta\)

theta

Answer Section#

Part 2#

Write the equation for Newton’s second law in the \(y\)-direction.

Note that it may not be necessary to use every variable. Use the following table as a reference for each variable:

For

Use

\(W\_{\textit{E on v}}\)

W

\(n\_{\textit{r on v}}\)

n

\(\theta\)

theta

Answer Section#

Part 3#

Solve the equations in Part 1 and Part 2 algebraically to determine the speed of the semi-truck.

Note that it may not be necessary to use every variable. Use the following table as a reference for each variable:

For

Use

\(m\)

m

\(g\)

g

\(\theta\)

theta

\(r\)

r

Answer Section#

Part 4#

Determine the speed of the semi-truck.

Answer Section#

Please enter in a numeric value in \(\rm{m/s}\)

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.