Newtons Laws of Motion and Resolving Forces

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Newtons Laws of Motion- and Resolving Forces
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Resolving Forces
All forces can be split into 2 perpendicular
forces
j
F
?
i
i direction
j direction
cos ? adj/hyp F1 / F
sin ? opp/hyp F2 / F
F1 F cos ?
F2 F sin ?
This process is known as Resolving Forces
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Resolving Forces and N2L
A sled (40kg) being towed by a rope (tension 30N)
at 25o, it accelerates at 0.5 ms-2. Find the
resistance (F) and the normal reaction.
N2L F ma weight 40g 40 x
9.8 392 N
30 N
Draw a Force diagram
The resultant horizontal force provides the
acceleration
N2L F ma Resultant 40 x 0.5 20N
Resolve horizontally
Resolve vertically
Resultant 30 cos 25 - F 20N 27.2 -
F 20 F 27.2 - 20 7.2N
R 30 sin 25 392 R 392 - 12.7 379.3 N
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Resolving Forces and N2L
A sled (50kg) being towed by a rope (tension 50N)
at 25o, has resistive force of 20N. Find the
acceleration
N2L F ma weight 50g 50 x
9.8 490 N
50 N
Draw a Force diagram
Resolve horizontally
Resultant 50 cos 25 - 20 45.3 - 20
25.3 N
N2L F ma Resultant 50 x a 25.3 50a
a 25.3 / 50 0.51 ms-2
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Activity

• Mechanics 1 book
• Exercise C page 89
• Q3 Kinematics and Fma
• Exercise D page 91
• Q1 Tension and Fma
• Exercise E page 93
• Q1 forces at an angle
• then the rest

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Newtons Laws of Motion- and slopes
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A Force Question - Reminder
Remember the Normal reaction is always
perpendicular to the slope
rope
R
Tension T
30o
In questions with slopes, it always works out
easiest to resolve forces parallel and
perpendicular to the slope.
30o
60o
30o
20 N
weight
Parallel to slope
Perpendicular to slope
R 20 cos 30 17.3 N
T 20 sin 30 10 N
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A slope and N2L problem (1)
An object of mass 2.8kg is pulled up a smooth
slope inclined at 40o by a light string parallel
to the slope. The object is accelerating at 0.5
ms-2. Find the tension in the string and the
normal reaction
0.5 ms-2
R
2.8 kg
T
0.5 ms-2
40o
N2L F ma weight 2.8g 2.8 x
9.8 27.44 N
40o
27.44 N
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A slope and N2L problem (2)
An object of mass 2.8kg is pulled up a smooth
slope inclined at 40o by a light string parallel
to the slope. The object is accelerating at 0.5
ms-2. Find the tension in the string and the
normal reaction
Resolve Parallel to slope
A resultant force must exist to make the object
accelerate
R
T
0.5 ms-2
Resultant force T - 27.44 cos 50 (T -
17.64) N
50o
N2L F ma Resultant 2.8 x 0.5 1.4 N
40o
27.44 N
So,
T - 17.64 1.4
T 1.4 17.64 19.0 N
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A slope and N2L problem (3)
An object of mass 2.8kg is pulled up a smooth
slope inclined at 40o by a light string parallel
to the slope. The object is accelerating at 0.5
ms-2. Find the tension in the string and the
normal reaction
Resolve Perpendicular to slope
No resultant force - acceleration is parallel to
slope
R
19 N
0.5 ms-2
R 27.44 sin 50 21.0 N
50o
40o
27.44 N
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KEY POINT FROM THIS LESSON
If an object is accelerating in a force question
then you need to used N2L to work out the
resultant force providing the acceleration
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Activity

• Mechanics 1 book
• Exercise G page 97
• Q 1 , 2, 3