Question

suppose that you have 2 boxes. one has a bottom of 0.25 m x 0.20 m and a mass of 55.5 kg. the other box has a bottom of 0.20 m x 0.40 m and a mass of 65.5 kg. find the pressure each box exerts on the ground and indicate which is the most​

Answer 1

Approximately
`1.1 * 10^(4)\; {\rm Pa}` and
`8.0 * 10^(3)\; {\rm Pa}`, respectively (assuming that
`g = 9.81\; {\rm N \cdot kg^(-1)}`.)

The
`55.5\; {\rm kg}` box exerts more pressure than the
`65.5\; {\rm kg}` box.

Step-by-step explanation:

Let
`m` denote the mass of the
`55.5\; {\rm kg}` box.

The weight of that box would be:
`W = m\, g`.

The normal force
`N` that this box exerts on the ground would be the same as its weight:
`N = W = m\, g`.

If the contact area between the box and the ground is
`A`, the pressure
`P` that this box exerts on the ground would be
`N / A`. That is:

`\displaystyle P = (N)/(A)= (m\, g)/(A)`.

The contact area between the ground and this
`55.5\; {\rm kg}` box is
`A = 0.25\; {\rm m} * 0.20\; {\rm m}`. Substitute in these values and evaluate to find the pressure:

`\begin{aligned} P &= (N)/(A) \\ &= (m\, g)/(A) \\ &= \frac{55.5\; {\rm kg} * 9.81\; {\rm N \cdot kg^(-1)}}{0.25\; {\rm m} * 0.20\; {\rm m}} \\ & \approx 1.1 * 10^(4)\; {\rm Pa}\end{aligned}`.

Similarly, for the
`65.5\; {\rm kg}` box:

`\begin{aligned} P &= (N)/(A) \\ &= (m\, g)/(A) \\ &= \frac{65.5\; {\rm kg} * 9.81\; {\rm N \cdot kg^(-1)}}{0.20\; {\rm m} * 0.40\; {\rm m}} \\ & \approx 8.0 * 10^(3)\; {\rm Pa}\end{aligned}`.

Thus, the
`55.5\; {\rm kg}` box exerts greater pressure on the ground than the
`65.5\; {\rm kg}` box.