# 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 $$r = {{ params.rad }}$$ $$\rm{m}$$.

## 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

## 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

## 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

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