You're driving your pickup truck around a curve with a radius of 22 m. 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?

Answer:

Explanation:

Centrifugal force Fc = m x v2 / r

Weight  = mg

As required by the question

Fc = W

v2 /r = g

given radius r = 22 m

v2 /22 = 9.8

Solve for v

required speed v = √(22 * 9.8)

= 14.35 m/s

v=15 m/s

this may help you

The force of the wall on the box equals the weight of the box when you drive with a speed of 14.68 m/s.

The centrifugal force can be described as an inertial force that appears to act on all objects in a rotating frame of reference. This force is directed away from an axis that is parallel to the axis of rotation and passes through the coordinate system's origin.

The magnitude of centrifugal force of mass m at the distance r from the origin rotating with angular velocity ω is:

[tex]{\displaystyle F=m\omega ^{2}r}[/tex]

Given, the radius of the curve, r = 22m

The acceleration, a = v²/r

The weight of the box, W = mg

We know that, F = ma

mg = m(v²/r)

v = √gr

[tex]\displaystyle v =\sqrt{9.8 \times 22}[/tex]

v = 14.68 m/s

Therefore, you should drive at a speed of 14.68 m/s

Learn more about centrifugal force, here:

https://brainly.com/question/17167298

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