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Chapter two FORCES AND MOTIONS
Chapter two
FORCES AND MOTIONS
Linear Motion
• Kinematics is the research regarding the types of movement of an object without referring to the forces that cause the movement of the object.
• Movement along a straight line is called linear motion.
• Under linear motion, we study the– distance and displacement– speed and velocity– acceleration
• and the relationship between them.
DistanceDefinition: The distance traveled by an object is the total length that is traveled by that object.
SI unit: meter (m)Quantity: Scalar
DisplacementDefinition: Displacement of an object from a point of reference, O is the shortest distance of the object from point O in a specific direction.
SI unit: meter (m)Quantity: Vector
Example:
The distance of point B from the origin O is 100m.The distance of point A from the origin O is also 100m.
The displacement of point B from the origin O is +100m.The distance of point A from the origin O is -100m.The + and – sign show the direction of the displacement.
Example:
Adli go to work by motorcycle everyday as shown in the diagram above.The distance that Adli travels from his house to the factory is 200m.The displacement of Adli from his house after arriving at the factory is 120m.
Speed
1.Speed is defined as the rate of change in distance. It is a measure of how fast the distance change in a movement.2.Speed is a scalar quantity.3.The SI unit of speed is m/s (metre per second)Equation of Speed
Velocity
1.Velocity is define as the rate of displacement change. It is the measure of how fast the displacement change of a moving object.2.Velocity is a vector quantity.3.The unit of velocity is m/s (metre per second)Equation of velocity
Positive or Negative Sign of Velocity
In velocity, the positive/negative sign indicates direction.
You can take any direction as positive and the opposite as negative.
For a linear motion, normally we take the motion to the right as positive and hence the motion to the left as negative.
Acceleration
Acceleration is defined as the rate of velocity change. It is a measure of how fast the velocity change.
Acceleration is a vector quantity.The unit of acceleration is ms-2.
An object moving with a velocity that is decreasing is said to be experiencing deceleration.
Example:A car travels from a stationary position and reach a velocity of 36 ms-1 in 8 seconds. What is the acceleration of the car?Answer:
Initial velocity, u = 0Final velocity, v = 36 ms-1
Time taken, t = 8sAcceleration, a = ?
Positive and Negative Sign of Acceleration1.Acceleration is a vector quantity, its sign (positive or negative) is determined by
a.its directionb.rate of change of the speed
2.If the speed of an object is increasing, the rate of change of the speed is positive, and if the speed of an object is decreasing, the rate of change of the speed is negative.3.Table below shows the positive/negative sign of acceleration related to the direction and rate of change of speed
a.When both the direction and change of speed are positive, the
acceleration is positive.
b.When the direction is positive and the change of speed is negative (speed decrease), then the acceleration is negative. This is equivalent to deceleration.
c.When the direction is negative and the change of speed is positive (speed increase), then the acceleration is also negative. Since the speed increase, hence this is not deceleration.
d.When both the direction and change of speed are negative, the acceleration is positive.
Additional Notes
*An object that experiences changes in velocity is said to have acceleration.*Changes of velocity can be
-change of speed-change of direction
*An object traveling with a constant acceleration, a, if the velocity changes at a constant rate.
Equation of Uniform Acceleration
Most of the motion problems can be solved by the following equations. Therefore, make sure that you memorise all of them. How we know when to use the equation?
Motion with Uniform Acceleration - Example 1
Example 1:An object accelerates from stationary with the acceleration of 4 ms-2. What is the velocity of the object after 7s?
Answer: It's advisable to list down all the information that we have.
Initial velocity, u = 0 (Because the motion start from stationary)Acceleration, a = 4 ms-2
Time taken, t = 7sFinal velocity, v = ?
The displacement, s, is not involved, hence we select the equation …………… to solve the problem.
Example 2A car is moving with velocity 5ms-1 reaches a velocity of 25ms-
1 in 5s. What is the acceleration of the car?
Answer: It's advisable to list down all the information that we have.
Initial velocity, u = 5ms-1
Final velocity, v = 25ms-1
Time taken, t = 5sAcceleration, a = ?
The displacement, s, is not involved, hence we select the equation ………………to solve the problem.
Example 3A cyclist riding at a speed of 40 ms-1 braked with uniform acceleration and stopped in 40m. How long did he take to stop?
Answer: It's advisable to list down all the information that we have.
Initial velocity, u = 40 ms-1
Final velocity, v = 0 (Because the cyclist stop)Displacement, s = 40mTime taken, t = ?
The acceleration, a, is not involved, hence we select the equation ...... To solve the problem.
Challenging Question 1:A car starts from rest and accelerates at a constant acceleration of 3 ms-2 for 10 seconds. The car then travels at a constant velocity for 5 seconds. The brakes are then applied and the car stops in 5 seconds. What is the total distance traveled by the car?
Answer: It's advisable to list down all the information that we have.
In this question, there are 3 stages of motion.
0s - 10sInitial velocity, u = 0 (Because the car start from rest)Acceleration, a = 3 ms-2
Time taken, t = 10sDisplacement, s = ?
10s - 15sIn this stage, the car moves with a constant velocity. The velocity is equal to the final velocity of previous stage. We can use the equation …………to determine the velocity.
Therefore, ………………….
15s - 20sIn this stage, the car undergoes deceleration.Initial velocity, u = 30 ms-1
Final velocity, v = 0 (The car stop at the end)Time taken, t = 5sDisplacement, s = ?
Total distance travelled = 150 + 150 + 75 = 375m
Ticker Tape Timer
1.A ticker tape timer consists of an electrical vibrator which vibrates 50 times per second or 50 hertz. 2.This enables it to make 50 dots per second on a ticker-tape being pulled through it. 3.The time interval between two adjacent dots on the ticker-tape is called one tick. 4.One tick or one dot-space (time interval) is equal to 1/50 s or 0.02 s.
The ticker time can be used to determine :- Diplacement of an object- Time interval of a motion- Velocity of an object- Acceleration of an object- Type of motion of an object
Example:Find the number of ticks and the time interval between the first dot and the last dot on each of the ticker tapes below. The frequency of the ticker timer is equal to 50Hz.a.
b.
c.
Answer: a. Number of ticks = 15, time interval = 15 x 0.02s = 0.3s
b. Number of ticks = 5, time interval = 5 x 0.02s = 0.1s
c. Number of ticks = 8, time interval = 8 x 0.02s = 0.16s
The distance between dots on a ticker tape The distance between two adjacent dots on a ticker-tape
represents the displacement of the object in a tick (0.02 s). If the object moves quickly, the dots are far apart. If the object
moves slowly, the dots are close to each other. Figure below shows the ticker-tapes produced by a fast and a
slow-moving object.
Ticker-tape charts
We can construct a ticker-tape charts by cutting the ticker-tape into length with an equal number of dots on each length and sticking the length side by side on a graph paper, in the same order that they were on the whole tape.The diagram below shows an example of ticker-tape chart. There are 10 ticks on each length. This means that each length represents a time interval of 0.2s.Ticker-tape charts are very useful in analyzing the motion of an object.
Analysing Ticker Tape
Uniform Velocity The distance of the dots is equally distributed.•All lengths of tape in the chart are of equal length.•The object is moving at a uniform velocity.
Uniform Acceleration
The distance between the dots increases uniformly.•The length of the strips of tape in the chart increase uniformly.•The velocity of the object is increasing uniformly, i.e. the object is moving at a constant acceleration.
Force
A force is push or pull exerted on an object.Force is a vector quantity that has magnitude and direction.
The unit of force is Newton ( or kgms-2).Unbalanced Force/ Resultant Force
When the forces acting on an object are not balanced, there must be a net force acting on it. The net force is known as the
unbalanced force or the resultant force.
When a force acts on an object, the effect can change thesize,shape,stationary state,speed anddirection of the object.
Newton's Second Law
The rate of change of momentum of a body is directly proportional to the resultant force acting on the body and is in the same direction.
Implication:
When there is resultant force acting on an object, the object will accelerate (moving faster, moving slower or change direction).
Newton's First Law:When there is no net force acting on an object, the object is either stationary or move with constant speed in a straight line.
Newton's Second Law:When there is a net force acting on an object, the object will accelerate.
Example 2A object of mass 50kg is placed on a horizontal floor with a smooth surface. If the velocity of the object changes from stationary to 25.0 m/s in 5 seconds when is acted by a force, find the magnitude of the force that is acting?
Answer:
We know that we can find the magnitude of a force by using the formula F = ma. The mass m is already given in the question, but the acceleration is not give directly.
We can determine the acceleration from the formula
Example 1A box of mass 150kg is placed on a horizontal floor with a smooth surface; find the acceleration of the box when a 300N force is acting on the box horizontally.
Answer:
F = ma(300) = (150)aa = 2 ms-2
Impulse
Impulse is defined as the product of the force (F) acting on an object and the time of action (t). Impulse exerted on an object is equal to the momentum change of the object. Impulse is a vector quantity.
Formula of impulse
Impulse is the product of force and time.
Impulse = F × t
Impulse = momentum change
Impulse = mv - mu
impulsive Force
Impulsive force is defined as the rate of change of momentum in a reaction.It is a force which acts on an object for a very short interval during a collision or explosion.
Example 1A car of mass 1000kg is traveling with a velocity of 25 m/s. The car hits a street lamp and is stopped in0.05 seconds. What is the impulsive force acting on the car during the crash?
Effects of impulse vs Force
A force determines the acceleration (rate of velocity change) of an object. A greater force produces a higher acceleration.An impulse determines the velocity change of an object. A greater impulse yield a higher velocity change.
Examples Involving Impulsive Force
Playing footballPlaying badmintonPlaying tennisPlaying golfPlaying baseball
