Question

A uniform box has a height, h, and a width, w. its center of mass at its geometric centre; ie it is h/2 above its base and w/2 to the right of its left side. which of the equations below gives the maximum angle you can tilt the box before gravity is able to make it tip over?

Answer 1

The maximum angle the box can be tilted before tipping over can be found using the equation: tan(θ) = (h/2) / (w/2).

Step-by-step explanation:

To find the maximum angle a box can be tilted before tipping over, we need to consider the box's center of mass and the base of support. When the center of mass is directly above the base of support, the box is in stable equilibrium. However, if the center of mass moves outside the base of support, the box will tip over.

In this case, the box has its center of mass at h/2 above its base and w/2 to the right of its left side. To calculate the maximum angle, we need to determine when the center of mass is at the edge of the base of support, which occurs when the horizontal distance from the center of mass to the edge is equal to w/2.

The maximum angle can be found using the trigonometric function tangent, where the tangent of the angle is equal to the height of the center of mass above the edge of the base divided by the horizontal distance from the center of mass to the edge. Therefore, the equation that gives the maximum angle is:
tan(θ) = (h/2) / (w/2)