SME
Grade 11 Science · Physics
Forces and Newton's laws: friction, inclines and tension
Use this for “A 120 N push moves a 20 kg box across a floor with μₖ = 0.3. What are the friction, the net force and the acceleration?”
Diagram
Weight = m × g = 20 × 9.8 = 196 N
Normal force = Weight = 196 N: nothing else pushes up or down.
f = μₖ × normal force = 0.3 × 196 = 58.8 N
Net force = F − f = 120 − 58.8 = 61.2 N
a = Net force/m = 61.2/20 = 3.06 m/s²
This is an example. Type your own values to start a new problem.
m
Mass
example
F
Applied force
example
μₖ
Coefficient of kinetic friction
example
W
Weight
calculated
FN
Normal force
worked out (not typed)
f
Friction
calculated
Fₙₑₜ
Net force
calculated
a
Acceleration
calculated · m/s²
Formulas
W
=
m
×
9.8
196 = 20 × 9.8
FN
=
W
196 = 196
f
=
μₖ
×
FN
58.8 = 0.3 × 196
Fₙₑₜ
=
F
−
f
61.2 = 120 − 58.8
a
=
Fₙₑₜ/
m
3.06 = 61.2/20
Assumptions
•
The push is level, and the block is already sliding, so friction is kinetic.
•
Up and down nothing moves: the normal force balances the weight.
•
Friction points against the motion; the net force is the push minus friction.
•
If friction is more than the push, a < 0: the sliding block slows down.
Step-by-step
WE KNOW
m = 20 kg, F = 120 N, μₖ = 0.3
FIND
weight (W), normal force (FN), friction (f), net force (Fₙₑₜ), acceleration (a)
Step 1 · Find weight (W)
Use W = m × 9.8
Earth pulls each kilogram with 9.8 N.
W
=
20
×
9.8
W
=
196
N
Step 2 · Find normal force (FN)
Use FN = W
Nothing else pushes up or down, so the floor pushes up with the weight.
FN = 196 N
Step 3 · Find friction (f)
Use f = μₖ × FN
Friction is μₖ times the normal force pressing the surfaces together.
f
=
0.3
×
196
f
=
58.8
N
Step 4 · Find net force (Fₙₑₜ)
Use Fₙₑₜ = F − f
The push forward less friction backward.
Fₙₑₜ = 120 − 58.8
Fₙₑₜ = 61.2 N
Step 5 · Find acceleration (a)
Use a = Fₙₑₜ/m
Newton’s second law: the net force over the mass.
a
=
61.2/20
a
=
3.06
m/
s
2
Check
Put the numbers back in. Both sides should match.
196 = 20 × 9.8 ✓
196 = 196 ✓
58.8 = 0.3 × 196 ✓
61.2 = 120 − 58.8 ✓
3.06 = 61.2/20 ✓
Topic check
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