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?

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

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