You're driving your pickup truck around a curve with a radius of 22meters. A box in the back of the truck is pressed up against the wall of the truck.

-How fast must you drive so that the force of the wall on the box equals the weight of the box?

V^2/R = gu

V = sqrt(R*g*u) = 13.133 m/s
u is the coefficent of static friction. Since this is steel on steel, u=0.1

Well, let me clarify a few things before providing a humorous response. Firstly, to determine the required speed, we need to consider the centripetal force acting on the box. This force is provided by the frictional force between the box and the wall of the truck. Secondly, the weight of the box will generate a downward force. Lastly, we need to know the mass of the box.

Now, onto the humor! If you really want the force of the wall on the box to equal its weight, you might consider driving at the speed of light. And while that might look impressive, I'm afraid that it won't end well for you or the box. Remember, speeding can lead to a lot of "centri-pain"! So, let's keep it safe and legal on the roads, shall we?

To find the speed at which the force of the wall on the box equals the weight of the box, we need to consider the equilibrium condition.

The force that keeps the box pressed against the truck's wall is the centripetal force (Fc), which is given by the equation:

Fc = (mv^2) / r

Where:
- m is the mass of the box
- v is the velocity of the truck
- r is the radius of the curve

Since we want the force of the truck's wall to be equal to the weight of the box, we can set up the equation:

Fc = mg

Where:
- m is the mass of the box
- g is the acceleration due to gravity

By equating those two equations, we have:

(mv^2) / r = mg

Next, we can simplify the equation by canceling out the mass (m) in each term:

v^2 / r = g

Rearranging the equation, we can solve for the velocity (v):

v = √(g * r)

Therefore, to find the speed at which the force of the wall on the box equals the weight of the box, you can substitute the values of the acceleration due to gravity (g) and the radius of the curve (r) into the equation and calculate the square root of their product.

If the centripetal force on the box equals the weight,

V^2/R = g
V = sqrt(R*g) = 14.7 m/s