A person in a descending lift can have a scale reading above their usual weight. When the lift moves downward and slows down, its acceleration points upward. The upward force from the scale must then exceed the person’s downward weight.
The scale measures the contact force it exerts on the person. For a 60 kg person with an upward acceleration of 1.2 m/s² and g = 9.8 N/kg, the scale force is 660 N.
- Find the direction of acceleration before choosing signs.
- Draw the weight and the upward contact force on the person.
- Use the resultant force to find the scale reading.
CHAPTER 1 OF 4 · Back to contents
Separate velocity from acceleration
Imagine the lift’s downward velocity changing from 3 m/s to 1 m/s. Its velocity is still downward, but it has changed in the upward direction. With upward taken as positive, the velocity changes from −3 m/s to −1 m/s.
Draw a force diagram for the person alone. Weight W = mg acts downward. The scale’s normal contact force N acts upward. Choose upward as positive, so the resultant is N − mg.
CHAPTER 2 OF 4 · Back to contents
Worked example | Find the scale force
The person’s weight is 60 × 9.8 = 588 N. The resultant force is ma = 60 × 1.2 = 72 N upward. Substitute into N − 588 = 72 to get N = 660 N.
As a check, N exceeds the weight by 72 N. That difference points upward and agrees with the acceleration. The gravitational force stays 588 N under the stated assumptions.
CHAPTER 3 OF 4 · Back to contents
Compare three phases of the same descent
If the lift speeds up downward at 1.2 m/s², the signed acceleration is −1.2 m/s². Then N − 588 = −72, giving 516 N. At constant downward speed, the acceleration is zero and N is 588 N. When it slows at 1.2 m/s², N is 660 N.
Imagine instead that the lift is moving upward and slowing down. Its acceleration points downward, so the scale force is below the weight. Work out the acceleration direction from the change in velocity each time.
CHAPTER 4 OF 4 · Back to contents
Frequently asked questions
Why can the resultant force point opposite to the motion?
The resultant points in the direction of acceleration. When an object slows in straight-line motion, the acceleration points opposite its velocity.
Does the person’s mass change?
The mass stays 60 kg. The changing reading reflects a change in the contact force.
What if the scale displays kilograms?
For an ideal scale calibrated using 9.8 N/kg, the 660 N reading corresponds to about 67 kg on its display. The force answer is 660 N.
Contents · Official syllabus and next practice
Official syllabus and next practice
Read the official SEAB 2027 syllabus
Practise drawing the two force arrows for constant speed, speeding up and slowing down.