# 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 van 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 van, $$\vec{n}_{\textit{r on v}}$$ is the normal force of the road on the van, and $$\vec{F}\_{\textit{net on v}}$$ is the net force on the van. Take the angle to be $$\theta = {{ params.ang }}^\circ$$ and the radius of curvature (distance from the centre of the circle to the van) to be $$r = {{ params.rad }}$$ $$\rm{m}$$.

## Part 1#

Write the equation for Newtonâ€™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

## Part 2#

Write the equation for Newtonâ€™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

## Part 3#

Solve the equations in Part 1 and Part 2 algebraically to determine the speed of the van.

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

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