Linear Motion

The motion that is natural to an object: moving in a straight line

Talking about linear motion scientifically, we need to talk about mass, distance, displacement, speed, velocity, and acceleration. 

MASS

The mass of a body refers to the amount of substance that it is made up of and is measured in kilograms (Kg). 

DISTANCE vs DISPLACEMENT

Distance ( d )is defined to be the magnitude or size of displacement between two positions - is a scalar measure of the spatial interval between two locations measured along the actual path connecting them..  

Displacement ( s ) is the change in position of an object                                                             - is a vector measure of the spatial interval between two locations measured along the shortest path connecting them.

The SI unit of distance and displacement is the meter [m]

DISTANCE PRACTICE

Distance = Speed x Time

1. How far can you get away from your big brother with the dodgeball if you can travel at 3 m/s and you have 15s before he hits you? 
2. Paul and Wendy want to ride their bikes from their neighborhood to school which is 14.4 kilometers away. It takes Amy 40 minutes to arrive at school. Paul arrives 20 minutes after Wendy How much faster (in meters/second) is Wendy's average speed for the entire trip? 

DISPLACEMENT PRACTICE

1: Find the following for path A:

(a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish.

2: Find the following for path B: 

(a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish.

3: Find the following for path C: 

(a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish.

4: Find the following for path D: 

(a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish.

Displacement Problem #2

SPEED vs VELOCITY

Speed ( v ) is defined to be the magnitude or the rate of change of its position                      - - speed is a scalar quantity and has only magnitude.

Speed = Distance/Time

Velocity ( V ) is the is speed with a direction or displacement/time in a direction                         - it is vector measure of the spatial interval between two locations measured along the shortest path connecting them.

The SI unit of speed and velocity is meters per second [m/s] or kilometres per hour km/h]

NOTE: Velocity can be zero, positive, or negative according to its displacement as zero, positive or negative.

SPEED PRACTICE

Will rolls a ball down a ramp until the ball hits the wall. The ramp is 2.5 m long and the distance from the end of the ramp to the wall is 1.5 m. If it took 0.5 seconds for the ball to hit the wall then what is the ball's speed? 

VELOCITY PRACTICE

Joanna took 0.75 hours to bicycle to his grandmother's house, a distance of 4 km. What is his velocity? 

ACCELERATION

Acceleration ( a ) is the rate at which a body changes its velocity and, similarly to velocity        - it is a vector quantity which means it has a direction as well as a magnitude. 

Acceleration = Velocity final - Velocity initial divided by time or (ms-2) = Vf - Vi (m/s) / time (s)

Acceleration (ms-2) = Force (N) / mass (kg)

The SI unit of It is measured in metres per second per second or metres per second squared - ms-2 [m/s/s]

ACCELERATION PRACTICE

1. If Michael Jordan has a vertical leap of 1.29 m, then what is his takeoff speed and his hang time (total time to move upwards to the peak and then return to the ground)? 

2.      A baseball is popped straight up into the air and has a hang-time of 6.25 s. Determine             the height to which the ball rises before it reaches its peak. (Hint: the time to rise to the           peak is one-half the total hang-time.)

Keep in mind that although acceleration is in the direction of the change in velocity, it is not always in the direction of motion. When an object slows down, its acceleration is opposite to the direction of its motion. This is known as deceleration. 

GRAVITY

Since gravity is a universal force that is always upon us it must be considered in regard to how it affects human movement. 

Gravity actually causes the body to move by its constant pull on the body's Centre of Mass also referred to as the Centre of Gravity (CoG). 

The Earth's gravitational force always pulls at a body's Centre Of Mass (CoM), whether it is the human body, a bowling ball, a car, etc. 

The human body moves when the CoG shifts away from the intersection point of three cardinal planes (Frontal, Sagittal, Transverse) of the body. 

This shift causes torque to be produced about the joints thus causing the body to move (locomotion). 

Acceleration of an implement while in flight is constant and always -9.8 meters/second squared or 32 ft/s2 (feet per second squared); the act of gravity on the implement. 

Therefore, generally all objects fall to the earth at the same rate of acceleration, no matter how much they weigh.

MOMENTUM

Momentum is a measure of the amount of motion a body has and is measured in units of kilogram metres per second (Kgm/s). 

 Linear momentum is defined as the product of a system's mass multiplied by its velocity

A rugby player mass 90Kg is running at 10m/s. What is the player's momentum?

momentum = 90Kg x 10m/s = 900Kgm/s

IMPULSE

To stop such an object, it is necessary to apply a force against its motion for a given period of time. 

This force is called IMPULSE

The more momentum that an object has, the harder that it is to stop. Thus, it would require a greater amount of force or a longer amount of time or both to bring such an object to a halt.  

TRY THESE:

1: An object that has a small mass and an object that has a large mass have the same momentum. Which object has the largest kinetic energy?

2: An object that has a small mass and an object that has a large mass have the same kinetic energy. Which mass has the largest momentum?

3: Football coaches advise players to block, hit, and tackle with their feet on the ground rather than by leaping through the air. Using the concepts of momentum, work, and energy, explain how a football player can be more effective with his feet on the ground.

4: How can a small force impart the same momentum to an object as a large force?