SME
Grade 8 Science · Problem type
Two skaters push apart: force pairs
Use this for “Two skaters push off each other. Who moves, and who speeds up more?”
Diagram
The push on A and the push on B are both 60 N, the opposite way
a₁ = F ÷ m₁ = 60 N ÷ 40 kg
= 1.5 m/s²
a₂ = F ÷ m₂ = 60 N ÷ 60 kg
= 1 m/s²
The lighter skater, A, speeds up more
This is an example. Type your own values to start a new problem.
a₁ (m/s²)
=
F (N)
÷
m₁ (kg)
a₂ (m/s²)
=
F (N)
÷
m₂ (kg)
Formulas
a₁
=
F
÷
m₁
(acceleration
of
A
=
push
÷
mass
of
A)
1.5 = 60 ÷ 40
a₂
=
F
÷
m₂
(acceleration
of
B
=
push
÷
mass
of
B)
1 = 60 ÷ 60
Assumptions
•
When A pushes B, B pushes A back with the same force the other way: the third law. It does not matter who “does” the pushing.
•
Both move: each speeds up by the push divided by its own mass, so the lighter skater speeds up more.
•
The ice is smooth enough that friction does not count.
Step-by-step
WE KNOW
F = 60 N (push), m₁ = 40 kg (mass of A), m₂ = 60 kg (mass of B)
FIND
acceleration of A (a₁), acceleration of B (a₂)
Step 1 · Find acceleration of A (a₁)
Use a₁ = F ÷ m₁ (acceleration of A = push ÷ mass of A)
A feels the whole push: divide it by A’s mass.
a₁
=
60
40
a₁
=
1.5
m/
s
2
Step 2 · Find acceleration of B (a₂)
Use a₂ = F ÷ m₂ (acceleration of B = push ÷ mass of B)
B feels the same push the other way: divide by B’s mass.
a₂
=
60
60
a₂
=
1
m/
s
2
Check
Put the numbers back in. Both sides should match.
1.5 = 60 ÷ 40 ✓
1 = 60 ÷ 60 ✓
Topic check
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Newton's three laws of motion
Main lesson
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