A ballerina weighs 103 lbs and is up on her toes with only 10.0 cm2 of her slippers in contact with the floor. What pressure is she exerting on the floor?

A

Explanation:

1 lb =.453 kg ... so ... 103 x. 453 = 46.72 kg

you then multiply that by the force of gravity which is 9.8 (m/s2) ... so ...

46.72 x 9.8 = 458 newtons (kg x m/s^2), which is the force.

pressure (in pascals) = Force (N) / Area (m2)

we need to convert 10cm2 to m2 which =.001m^2

458 /.001 = 458000 = 4.58 x 10^5 Pa

Options for the question;

A. 4.59 * 105 Pa

B. 4.59 * 103 Pa

C. 4.59 * 101 Pa

D. 4.59 * 10ˉ1 Pa

E. 4.59 * 10ˉ3 Pa

Answer:

Pressure = 458000 = 4.58 x 10^5 Pa; Option A

Explanation:

Bringing out the parameters in the question;

Weight = 103 lbs = 46.72 kg (Upon conversion by diving by 2.205)

Area occupied = 10.0 cm2 = 0.001m2 (Upon conversion by dividing by 10000)

Pressure = ?

The relationship between pressure and Area is given as;

Pressure (in pascals) = Force (N) / Area (m2)

Force = Mass * Gravity = 46.72 * 9.8 = 458 N

Pressure = 458 / 0.001 = 458000 = 4.58 x 10^5 Pa