Schaum's 3000 Solved Problems in Physics · Problem 4.10 · Newton's laws

Two masses, fastened together

Accelerations do not add. Masses do.

A resultant force of 20 N gives a body of mass m an acceleration of 8.0 m/s², and a body of mass m′ an acceleration of 24 m/s². What acceleration will this force cause the two masses to acquire if fastened together?as printed, page 52

Tap any symbol, here or in a formula, to see what it is and its value.

The picture
m 2.5 kg 20 N · 8 m/s² m′ 20 N · 24 m/s² 3.33 kg 20 N · 6 m/s²
time0.00 s
m alone0.0 m
m′ alone0.0 m
together0.0 m
Feel the numbers
2.5 kgthe mass of m

A bag of sugar and a bit. Twenty newtons gets it to 8 m/s in one second.

0.83 kgthe mass of m′

A litre of water, nearly. Same push, three times the acceleration, because a third the mass.

6.0 m/s²fastened together

Not 8 plus 24, not the average. Add the masses, then divide. The pair is heavier than either, so it accelerates less than either.

The walkthrough

Press play and it reads straight through, scrolling as it goes. Space pauses. ← → move a step. ▶ on a step plays from there.

Every symbol
Narrated by the Listen voice. Timing comes from the narration itself, so the light lands on the part of the formula that is being said.
epicnotes