Question

(a) When you step on a weighing scale set on a level ground, is the scale’s reading a true measure of your weight? (b) Would the scale reading differ when the scale is set on a sloping surface? Clearly explain your answers using Newton’s 3rd law of motion.

Answer 1

$\text(a)$

$\text{The weight P is equal to the force of gravity acting on the body}$

$\text{and is proportional to the mass and the acceleration of gravity.}$

$\vec P = m\vec g$

$\text{The weighing scales show the value }m.$

$\text{Answer: No}$

$(b)$

$\text{The scales, according to Newton's 3 law, act on a body with a}$

$\text{force } \vec F_1\text{ equal to the force of action }\vec F\text{ of the body on the scales}$

$\text{and opposite in direction}.$

$\vec{F_1}=-\vec{F}$

$\vec F \text{ this is the projection of } \vec P \text{ onto the axis perpendicular to the slope}$

$|\vec F|<|\vec P|$

$|\vec F_1|<|\vec P|$

$\text{Answer: The scales will be understated.}$