Force and Motion

Prior Concepts Related to Forces PreK-2 Forces are pushes and pulls that change the motion of an object. Forces are required to change the motion of an object. Greater force on a given object result in greater changes of motion.

Prior Concepts Related to Forces Grades 3-5 The amount of change in movement of an object is based on the mass of the object and the amount of force exerted.

Prior Concepts Related to Forces Grades 6-7 An object’s motion can be described by its speed and the direction in which it is moving. An object’s position and speed can be measured and graphed as a function of time.

Position (x) The location of an object at a given time. X i - initial position X f - final position

Delta = Δ The Greek letter that means change.

Motion The act of changing position.

Change of position = Δx

Displacement (Δx) Change of position in a direction. (positive or negative) Δ x = x f – x i

The motion of an object is always measured with respect to a reference point. Motion can be described in different ways by different observers (e.g., a pencil held in someone’s hand may appear to be at rest, but to an observer in a car speeding by, the pencil may appear to be moving backward).

Relative Motion Relative motion is the calculation of the motion of an object with regard to some other moving object. Thus, the motion is not calculated with reference to the earth, but is the velocity of the object in reference to the other moving object as if it were in a static state.

Relative Motion Introduction YVzc YVzc

Mythbusters - Soccer Ball Shot from Truck zc&list=PLtXf78zN40CLmbhE_3frrac6_yTqO8B oL zc&list=PLtXf78zN40CLmbhE_3frrac6_yTqO8B oL

Distance = d The amount of change of position.

Reference Point A specific location on an object or in an object’s environment used to monitor change of position.

Equation for calculating distance (d) when initial ( x i ) and final ( x f ) positions are known. d = x f – x i

Speed (v) The distance an object travels in a unit of time.

Average speed is the total distance traveled by an object divided by the total time from start to finish.

Speed Definitions: –Speed The rate at which something moves a given distance. Faster speeds = greater distances –General formula for speed: Speed = distance / time Abbreviations commonly used: – d = distance t = time v = speed v = d/t

Equation for calculating speed (v) when distance and time are known v = d / Δt

Equation for calculating distance (d) when speed and time are known. d = v Δt

Equation for calculating time (t) when speed and distance are known Δt = d/v

Speed Graph

Object NOT moving

If an object is moving at a constant speed, it means it has the same increase in distance in a given time: Time is increasing to the right, and distance is increasing constantly with time. The object moves at a constant speed. Constant speed is shown by straight lines on a graph. A steeper line indicates a larger distance moved in a given time. In other words, higher speed.

The line on the graph below is curving upwards. This shows an increase in speed, since the line is getting steeper: In other words, in a given time, the distance the object moves is changing (getting larger). It is accelerating. (Acceleration=speeding up or slowing down) Ac

Position Graph

Velocity (v) The rate at which an object changes position over time in a given direction.

Acceleration (a) A change of velocity per unit of time.

Acceleration is measured in units of displacement per unit of time per unit of time. (meters per second per second or m/s/s or m/s 2 ) Change in speed Time

Kinetic Friction is a force that occurs when two objects in contact interact by sliding past one another

Static friction is the friction that exists between a stationary object and the surface on which it's resting.

Forces have magnitude and direction. (magnitude = amount of force, Newtons)

The motion of an object is always measured with respect to a reference point.

Relative Motion Relative motion is the calculation of the motion of an object with regard to some other moving object. Thus, the motion is not calculated with reference to the earth, but is the velocity of the object in reference to the other moving object as if it were in a static state.

Relative Motion

If the plane encounters a headwind, the resulting velocity will be less than 100 km/hr. Since a headwind is a wind that approaches the plane from the front, such a wind would decrease the plane's resulting velocity. Suppose a plane traveling with a velocity of 100 km/hr with respect to the air meets a headwind with a velocity of 25 km/hr. In this case, the resultant velocity would be 75 km/hr; this is the velocity of the plane relative to an observer on the ground.

Relative Motion Now consider a plane traveling with a velocity of 100 km/hr, South that encounters a side wind of 25 km/hr, West. Now what would the resulting velocity of the plane be? This question can be answered in the same manner as the previous questions. The resulting velocity of the plane is the vector sum of the two individual velocities. To determine the resultant velocity, the plane velocity (relative to the air) must be added to the wind velocity. This is the same procedure that was used above for the headwind and the tailwind situations; only now, the resultant is not as easily computed. Since the two vectors to be added - the southward plane velocity and the westward wind velocity - are at right angles to each other, the Pythagorean theorem can be used.

The correct answer is D. This is a problem concerning relative motion. Someone standing on the side of the road would see Car A traveling at 30 km/hr and Car B traveling at 50 km/hr because compared to the ground this is how fast the cars are moving. However someone in Car A (Car A is now the frame of reference) would see Car B traveling at 80 km/hr traveling towards him. When objects are traveling in opposite directions and one of them is the frame of reference, the speeds add and the direction of the object being observed will be the same as its direction compared to the ground. If the objects are traveling in the same direction, the speeds will subtract. The direction the observed object will appear to travel will depend on how the speeds compare. If the speed of the frame of reference is greater than the observed object, the object will appear to move in the opposite direction to its motion compared to the ground. If the frame of reference is moving at a speed less than the object, then the object will appear to be traveling in its original direction, only slower.

Relative Motion

The plane sees the horse traveling at 12 m/s east. The runner sees the horse traveling at 12 m/s west. The cylist sees the horse traveling at 22 m/s west. Therefore, the correct answer is D.

The correct answer is C. In this case, we are given the velocity of the rhino compared to the ground and the velocity of the tickbird compare to the rhino. We are asked to find the velocity of the tickbird to the ground, which is the opposite of what you were asked to find in Questions 2 and 3. When asked to find a velocity relative to the ground, algebraically add the given velocities. Assume the the rhino is moving toward the west at - 1 m/s and that the tickbird is moving at m/s, because he is moving in the opposite direction. Add the two numbers to get the relative velocity of the tickbird to the ground. -1 m/s m/s = m/s. The tickbird appears to be moving at 0.75 m/s toward the west.

Forces can be added. The net force on an object is the sum of all of the forces acting on the object. The net force acting on an object can change the object’s direction and/or speed.

Force Diagrams

When the net force is greater than zero, the object’s speed and/or direction will change. Or Any nonzero net force, including negative net force, may result in a change in speed or direction (acceleration).

When the net force is zero, the object remains at rest or continues to move at a constant speed in a straight line.

Forces A force is described by its strength (magnitude) and in what direction it is acting.

A force is a push or a pull. Forces acting in the same direction add together; forces acting in opposite directions subtract.

If the force of a pull exerted on one side of an object is greater than the force of a pull exerted on the other side of an object, the object will move toward the larger force. (unbalanced force or nonzero net force)

Inertia The property of mass that resists change of motion. Large masses have a lot of inertia.

Newton’s First Law If the net force acting on an object is zero, the object will remain at rest or move in a straight line with a constant speed.

Newton’s Second Law An object acted upon by a net force will accelerate in the direction of the force, and that the acceleration equals the net force divided by the object’s mass. F net =m x a

Newton’s Third Law Forces always act in equal and opposite pairs.

Net force is the sum of all the forces acting on a mass.

If equal forces are exerted on an object in opposite directions, the object’s motion will not change. (we say we have a balanced force or a net force of zero) Objects in motion would stay in motion and objects at rest would stay at rest.

Friction is a force that resist movement. Kinetic friction is a force that occurs when two objects in contact interact by sliding pas one another. Force is measured in newtons (N).

An unbalanced force acting on an object changes that object’s speed and/or direction.

A net force (unbalance force) applied to a mass results in acceleration. If the net force is positive, the object moves to the right. If the net force is negative, the object moves to the left. If the net force is zero, no change of motion results. (balance forces)

Acceleration (a) A change of velocity per unit of time.

Acceleration is measured in units of displacement per unit of time per unit of time. (meters per second per second or m/s/s or m/s 2 ) Change in speed Time