F = ma problems: lifts, tow bars and slopes

5 minAS Level3.1.23.1.53.1.6

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can solve multi-force problems with $F = ma$ : lifts, objects pulling each other along, and objects on slopes.

The four-step method

Most dynamics problems fold in the face of the same four steps:

Choose the object (or group of objects) you'll apply $F = ma$ to.
Draw its free-body diagram: every force acting on it, and nothing else. Usual suspects: weight $mg$ , tension, normal contact force, friction, drag, driving force.
Take the direction of the acceleration as positive and write the resultant: forces that way minus forces the other way.
Set the resultant equal to $ma$ and solve. Add suvat if the question wants a speed, a distance or a time.

Lifts

Upwards positive. For a lift of mass $m$ hanging from a cable with tension $T$ :

$T - mg = ma$

What the lift is doing	Acceleration	Tension
speeding up going up, or slowing down going down	upwards	$T > mg$
at rest, or constant velocity	zero	$T = mg$
speeding up going down, or slowing down going up	downwards	$T < mg$

The same goes for you standing in the lift: the floor's contact force $R$ obeys $R - mg = ma$ . That's why you feel heavier as a lift sets off upwards. Bathroom scales measure that contact force, not your weight, so at that moment they'd read more than your weight.

Worked example: A lift setting off upwards

A lift of total mass $800\ \text{kg}$ accelerates upwards from rest at $1.5\ \text{m s}^{-2}$ . Find the tension in the cable.

Have a go first?

Quick check

CalculateQuestion 1 · Apply

Multiple choiceQuestion 2 · Apply

Answer the 3 questions above to continue.