Hand Supports a Mass

The standard acceleration of gravity (at sea level and 45° latitude) is 9.80665 m/s². At that location
a) Calculate the force is required of a hand to support at rest a mass of 2 kilograms.
b) Calculate the mass a force of one Newton could support.

Effects of the ever-present atmospheric air are often negligibly small. We assume ρ_air ~ 0. Sonntag ~ pg 35, prob 27.

♦ Our system is some mass of 2 kilograms that is supported by a person's hand. The image (above right) is a scenario of this event.

To apply Newton's Second Law of Motion requires a "system schematic." The mass must be isolated and the forces shown. See the free body diagram below right. Sonntag assumes, without statement, that no effect of atmospheric pressure is involved. Hand Mass FBD A system sketch (FBD) of the scenario mass
modeled as a BODY. The density of ambient
air is assumed negligible.

The forces are those of gravity and the hand. Newton's Second Law for the mass with these two forces is:

(1) 1

The velocity of the mass is zero. Only vertical forces act so we scalar multiply Newton's equation by K.

(2) 2

Next we use the fact, K • K = 1. We enter the surface acceleration and solve for the magnitude of the force:

(3)

♦ The next part asks the mass that a force of 1.0 Newton could support. We use the equation (2) from above:

(4) 4

This problem is from Sonntag. It is misleading and a waste of time to carry such precision. A device that could measure a force to the precision of 19.61330 Newtons or a device that could measure a mass of 0.1019716 kilograms would cost millions of pounds "cash."