Download Badger Chapter 28 - Forces and Motion

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28
Forces and Motion
GCSE
A-level
You will have covered examples of
forces and how unbalanced forces
affect motion.
You need to be able to use Newton’s Second Law
of Motion to calculate acceleration.
Balanced forces
Objects with no resultant force acting on them are in equilibrium. They continue in their state of
motion, whether at rest or at a constant speed in a straight line.
To change the motion of an object, there must be an overall force acting: a resultant or net force.
It is the forces acting on an object that determine its motion.
What does Newton’s First Law of Motion tell us?
A body remains at rest, or continues to move with constant velocity in a straight line, unless a
resultant force acts.
In such a case, the sum of forces = zero.
What does Newton’s Second Law of Motion tell us?
The acceleration of an object is directly proportional to the resultant force applied, and inversely
proportional to the mass of the object.
F ma
Units: force in newtons (N); mass in kilograms (kg); acceleration in metres per second per second
(ms2)
The sum of forces = mass acceleration.
Example Problems
1
2
A jet engine produces a thrust of 20.0 kN. What acceleration is produced when the jet is
attached to a vehicle of 2.6 103 kg?
F 20 000 N
m 2.6 103 kg
F ma so a F
20 000
7.7 msⴚ2
m
2.6 103
a=?
How much force is experienced when a 50 kg man is subjected to 8 g of acceleration?
m 50 kg
a 8 9.8 78.4 ms2
F ma = 50 78.4 3920 N
Weight
Weight is a force, and it is calculated by multiplying a mass by an acceleration (the acceleration
due to gravity). Weight is a particular case of the Second Law of Motion.
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Forces and Motion
Problems involving unbalanced forces are treated the same way as problems with balanced forces
except that the forces in the direction of motion now add to mass x acceleration rather than zero.
Follow the steps below:
•
Draw a diagram of the situation, with all forces drawn on it and labelled. Add a separate
arrow for acceleration (not attached to object but next to it).
•
Select axes – usually x horizontal and y vertical.
•
Any force not parallel to one of the axes needs to be resolved into its component vectors.
•
All forces in the vertical direction sum up to the mass acceleration in that direction;
remember and signs, depending on direction.
•
All forces in the horizontal direction sum up to the mass acceleration in that direction;
remember and signs, depending on direction.
•
Solve for any unknown values.
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Forces problems
Example
A set of scales is placed in a lift that travels up to a weight-loss club. The lift accelerates at
1.4 ms2 whether speeding up or slowing down in either direction. A person of mass 80 kg stands
on the scales. Calculate:
a.
b.
c.
d.
The reading on the scales when the lift is stationary
The reading on the scales when the lift is accelerating upwards at 1.4 ms2
The reading on the scales when the lift is accelerating downwards at 1.4 ms2
The reading on the scales when the lift is travelling at a constant velocity
a = 1.4 ms-2
R
a = 1.4 ms-2
mg
a. When stationary, forces sum up to zero: R mg 0
R mg 80 9.8 784 N
b. Accelerating upwards so a 1.4 ms2; forces sum up to ma:
R mg ma; R ma mg 80 1.4 80 9.8 896 N
c. Accelerating downwards so a 1.4 ms2; forces sum up to ma:
R mg = ma;
R ma mg 80 (1.4 ) 80 9.8 672 N
d. When travelling at a constant velocity, forces sum up to zero:
R mg = 0;
R mg = 80 9.8 784 N
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Topic Builders
28
Forces and Motion
Questions
g 9.8 ms2
1
State Newton’s First Law of Motion.
2
Write an equation that represents Newton’s Second Law of Motion.
3
Calculate the force required to accelerate a mass of 20 kg by 54 ms2.
4
Calculate the force required to accelerate a mass of 2 g by 890 ms2.
5
What mass accelerates at 4.7 ms2 when a resultant force of 15 N is applied?
6
What mass accelerates at 205 ms2 when a resultant force of 46 kN is applied?
7
What acceleration would a 50 g mass have if it were acted on by a resultant force of
80 N?
8
What acceleration would a 1000 kg mass have if it were acted on by a resultant force
of 2.3 N?
9
A lift car of mass 1200 kg accelerates at 2 ms2 when speeding up or slowing down.
Calculate the tension in the lift cable when the lift is:
a. at rest
b. accelerating upwards
c. accelerating downwards
Taking it Further
The ideas discussed and used here are essential for understanding mechanics and motion.
Now use this space to make more in-depth notes about forces and motion. Some questions have
been suggested to help you structure your notes effectively. You may wish to also use your course
textbook to add further information to your notes.
Ÿ What is Newton’s First Law of Motion?
Ÿ What is Newton’s Second Law of Motion?
Ÿ How is mass related to weight?
Ÿ How can acceleration explain weightlessness in orbit?
Ÿ What is the value of the acceleration due to gravity on the surface of other planets?
Ÿ How does acceleration due to gravity on the surface of a planet vary with mass and radius
of the planet?
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