Vertical Equilibrium & The Normal Force Practice Problems

A kid's knees are initially on the ground (like in a kneeling position). Upon hopping straight from this state, the kid can reach a height of about 20 cm. While making the hop, his body rises a distance of 16 cm from the knees up. Assume that this is true for his entire body as well. Solve for the force F that the ground exerts on the kid during the hop. Express this in terms of the kid's weight, w.

In a warehouse, a 30.0-kg wooden crate is placed on a sturdy table. A 20.0-kg metal box is then placed on top of the wooden crate as shown. Determine the normal force that the table exerts on the wooden crate and the normal force that the wooden crate exerts on the metal box.

A 90-kg woman steps onto an aluminum rod with a radius of 𝑅=20 cm and a length 𝐿, which stands firmly on a concrete floor. The aluminum atoms in the rod are normally 2.5 × 10^-10 meters apart. By what distance must this interatomic spacing change to produce the normal force required to support the woman? The Young's modulus 𝐸 for aluminum is $70 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$

Consider a 950-kg truck kept stationary by a light rope on a frictionless slope as shown in the figure. The rope forms an angle of 28° with the slope's surface, and the slope is angled at 20.0° relative to the horizontal. Determine the magnitude of the normal force exerted by the slope on the truck.