Weight & vertical motion | CAIE 9709 Mechanics Notes

Mechanics

Mathematics9709

Keep mass and weight separate

Definition

What is meant by weight?

Model answer: The gravitational force acting on a body, equal to its mass multiplied by the acceleration due to gravity.

W=mg

Symbols

$W$ = weight (N)
$m$ = mass (kg)
$g$ = acceleration due to gravity; use 10 unless told otherwise (m s⁻²)

Mass is measured in kilograms; weight is measured in newtons.
A particle of mass $m$ has weight $10m$ N in this Mechanics component.
In free fall with no resistance, $mg=ma$ , so $a=g$ . The mass cancels.

Weight stays downward; resistance opposes the motion

Swipe left or right to see the whole diagram →

Weight keeps the same direction. Resistance changes direction when the motion reverses, so a new force diagram and a new acceleration are required.

Suppose a ball of mass 2 kg experiences a constant resistance of 4 N. While it moves upward, both weight and resistance act downward. Taking upward as positive:

-20-4=2a

a=-12\text{ m s}^{-2}

After the ball begins to move downward, resistance points upward. Keeping upward positive:

4-20=2a

a=-8\text{ m s}^{-2}

Key idea

The acceleration can be different immediately before and immediately after the direction reverses. Redraw resistance for the new direction of motion instead of carrying the earlier force diagram forward.

A support force is not automatically equal to weight

For a passenger of mass $m$ in a lift, the floor exerts anormal reaction $R$ : the contact force from the floor, perpendicular to the floor. Taking upward as positive gives:

R-mg=ma

If $a=0$ , then $R=mg$ .
If acceleration is upward, $R>mg$ .
If acceleration is downward, $R<mg$ .
Contact requires $R\ge 0$ . A negative calculated reaction means the assumed contact model is impossible.

Your turnIndependent check [5 marks]

A 60 kg passenger stands on the floor of a lift. Find the normal reaction on the passenger when the lift accelerates (a) upward at 1.5 m s⁻², (b) downward at 1.5 m s⁻², and (c) moves upward at constant speed.

Show worked answer

Take upward as positive and use $R-600=60a$ .

R=600+60(1.5)=690\text{ N}

R=600+60(-1.5)=510\text{ N}

R=600\text{ N}

Answer

690\text{ N}

510\text{ N}

600\text{ N}