Calculating forces
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Gravity & Newton’s third law
Tension & pulleys
Car towing a trailer
Inclined planes
Calculating forces - 1
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Earth’s gravitat
Gravity & Newton’s third law
• The forces on a stationary object are not an action reaction pair.
• (Action reaction pairs act on different objects).
• The Earth pulls down on the box. The box pulls up on the Earth.
• The box pushes down on the surface (contact force). The surface
pushes up on the box.
Surface pushes up on box
(Normal reaction force)
Normal reaction force (N)
Box pushes down on surface
Earth’s gravitational pull
acts down on box
Weight (mg)
Calculating forces - 2
Box’s gravitational pull
acts up on the Earth
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Tension & pulleys
• Two weights on a pulley: 4 kg & 10 kg.
• What is the acceleration of the system?
• What is the tension in the string?
Tension: pulls up on m1
T
& against m2
ΣF 100 N - 40 N
a=
=
m 10 kg + 4 kg
60 N
a=
14 kg
g(m2 - m1 )
a=
(m2 + m1 )
a = 4.3 m/s2
m1
ΣF = m1a = T - m1g
40 N
∑F = 4.0 kg ×4.3 m/s
= 17 N
T = m1a + m1g
2
m2
T = m1(g + a)
T = (4.0 kg ×4.3 m/s2 ) + 40 N = 57 N
100 N
Calculating forces - 3
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Car towing a trailer
• What is the acceleration?
• What is the tension force pulling forward on the trailer?
m = 1000 kg
m = 2000 kg
T
1800 N
T
1200 N
6000 N
6000 N - 3000 N
Trailer:
Car:
a=
3000 kg
∑F =ma =1000kg ×1.0m /s 2 ∑F =ma =2000kg ×1.0m /s 2
∑F =1000N
∑F =2000N
3000 N
a=
1000N =T −1800N
2000N = 6000N −1200N −T
3000 kg
T =2800N (forward)
T =2800N (back)
a =1.0 m/s2
Calculating forces - 4
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Inclined planes
• An object at rest on an inclined plane has all forces adding to zero.
• The weight force (acting straight down) can be resolved into two
components.
N
mg = 2000 kg ×10 N/kg = 20,000 N
mg = 20kN
N = mg cosθ
N = 20 kN ×cos15°
N = 19.3 kN
friction
15°
mg
15°
Friction = mg sinθ
Friction = 20 kN × sin15°
Friction = 5.2 kN
mg cos 15° (perpendicular to slope)
m = 2000 kg
mg sin 15° (parallel to slope)
Calculating forces - 5
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