Question

explain the following with the help of a directions at the same


depth

Answer 1

Answer:

If you tried to hammer a bowling pin into the wall, nothing would probably happen except for people deciding to no longer lend you their bowling pins. However, if you hammer with the same force on a nail, the nail would be a lot more likely to penetrate the wall. This shows that sometimes just knowing the magnitude of the force isn't enough: you also have to know how that force is distributed on the surface of impact. For the nail, all the force between the wall and the nail was concentrated into the very small area on the sharp tip of the nail. However, for the bowling pin the area touching the wall was much larger, and therefore the force was much less concentrated.

Example 1: Finding the pressure from the feet of a chair

A 7.20 kg7.20 \text{ kg}7.20 kg7, point, 20, space, k, g fuchsia colored four legged chair sits at rest on the floor. Each leg of the chair has a circular foot with a radius of 1.30cm1.30\text{cm}1.30cm1, point, 30, c, m. The well engineered design of the chair is such that the weight of the chair is equally distributed on the four feet.

Find the pressure in pascals between the feet of the chair and the floor.

P=FA(Use definition of pressure. Gauge pressure isn’t applicable here since there’s no fluid.)P=\dfrac{F}{A} \quad \text{(Use definition of pressure. Gauge pressure isn't applicable here since there's no fluid.)}P=A

F​(Use definition of pressure. Gauge pressure isn’t applicable here since there’s no fluid.)P, equals, start fraction, F, divided by, A, end fraction, space, left parenthesis, U, s, e, space, d, e, f, i, n, i, t, i, o, n, space, o, f, space, p, r, e, s, s, u, r, e, point, space, G, a, u, g, e, space, p, r, e, s, s, u, r, e, space, i, s, n, apostrophe, t, space, a, p, p, l, i, c, a, b, l, e, space, h, e, r, e, space, s, i, n, c, e, space, t, h, e, r, e, apostrophe, s, space, n, o, space, f, l, u, i, d, point, right parenthesis

P=mgA(Plug in formula for weight of the chair W=mg for the force F)P=\dfrac{mg}{A} \quad \text{(Plug in formula for weight of the chair } W=mg \text{ for the force F)}P=A

mg​(Plug in formula for weight of the chair W=mg for the force F)P, equals, start fraction, m, g, divided by, A, end fraction, space, left parenthesis, P, l, u, g, space, i, n, space, f, o, r, m, u, l, a, space, f, o, r, space, w, e, i, g, h, t, space, o, f, space, t, h, e, space, c, h, a, i, r, space, W, equals, m, g, space, f, o, r, space, t, h, e, space, f, o, r, c, e, space, F, right parenthesis

P=mg4×πr2(Plug in the total area of the feet of the chair  for the area A.)4×πr2P=\dfrac{mg}{4\times \pi r^2} \quad \text{(Plug in the total area of the feet of the chair $4\times \pi r^2$ for the area A.)}P=4×πr2

mg​(Plug in the total area of the feet of the chair 4×πr2 for the area A.)P, equals, start fraction, m, g, divided by, 4, times, pi, r, start superscript, 2, end superscript, end fraction, space, left parenthesis, P, l, u, g, space, i, n, space, t, h, e, space, t, o, t, a, l, space, a, r, e, a, space, o, f, space, t, h, e, space, f, e, e, t, space, o, f, space, t, h, e, space, c, h, a, i, r, space, 4, times, pi, r, start superscript, 2, end superscript, space, f, o, r, space, t, h, e, space, a, r, e, a, space, A, point, right parenthesis

P=(7.20 kg)(9.8ms2)4×π(0.013 m)2(Plug in numbers, making sure to convert from cm to m)P=\dfrac{(7.20\text{ kg})(9.8\dfrac{\text{m}}{\text{s}^2})}{4\times \pi (0.013\text{ m})^2} \quad \text{(Plug in numbers, making sure to convert from cm to m)}P=4×π(0.013 m)2

(7.20 kg)(9.8s2

m​)​(Plug in numbers, making sure to convert from cm to m)P, equals, start fraction, left parenthesis, 7, point, 20, space, k, g, right parenthesis, left parenthesis, 9, point, 8, start fraction, m, divided by, s, start superscript, 2, end superscript, end fraction, right parenthesis, divided by, 4, times, pi, left parenthesis, 0, point, 013, space, m, right parenthesis, start superscript, 2, end superscript, end fraction, space, left parenthesis, P, l, u, g, space, i, n, space, n, u, m, b, e, r, s, comma, space, m, a, k, i, n, g, space, s, u, r, e, space, t, o, space, c, o, n, v, e, r, t, space, f, r, o, m, space, c, m, space, t, o, space, m, right parenthesis

P=70.56 N0.002124 m2=33,200 Pa(Calculate, celebrate!)P=\dfrac{70.56 \text{ N}}{0.002124 \text{ m}^2}=33,200 \text{ Pa} \quad \text{(Calculate, celebrate!)}P=0.002124 m2

70.56 N​=33,200 Pa(Calculate, celebrate!)

Explanation: