Hand Supports a Mass

Basic Thermodynamics ~ J. Pohl ©

www.THERMOspokenhere.com (33-A330)

A physical scenario.

The "standard" acceleration of gravity (at sea level and 45° latitude) is 9.80665 m/s².

a) What force is required to hold a mass of 2 kilograms at rest in this
gravitational field?
b) Also, How much mass can a force of one Newton support?

Note: This problem statement, (Sonntag, pg 35 Prob 27) makes no statement regarding the surrounding atmosphere. Effects of the ever-present atmospheric air are often negligibly small. Hence we assume ρ_air ~ 0.

♦ 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. 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) This precision is a waste of time.

♦ 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.