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In Motion Physics for Science 20F ihCA9E

Distance vs. Displacement difference between a scalar and a vector. difference between a scalar and a vector. A Scalar is a value - has only a number & a unitex: 25km, 150lbs A Scalar is a value - has only a number & a unitex: 25km, 150lbs A Vector - value that has a number, unit and a direction A Vector - value that has a number, unit and a direction ex: 30 cm left, 40km north (N)

Distance is how far you’ve traveled in total Distance is how far you’ve traveled in total ex: 25 km Displacement is how far you are from your starting point. This needs a direction Displacement is how far you are from your starting point. This needs a direction ex: 25 km from home or 40km north of the city So, distance is a scalar value whereas displacement is a vector. So, distance is a scalar value whereas displacement is a vector.

Displacement with respect to time… Displacement with respect to time… Displacement - always calculated by Displacement - always calculated by final position minus initial position. final position minus initial position.

Positive/negative displacement A line going up A line going up to the right is a positive to the right is a positive A line going down A line going down to the right is a negative. Draw it. to the right is a negative. Draw it. A flat line represents no displacement A flat line represents no displacement (like you’re standing still). Draw it. (like you’re standing still). Draw it. We need to translate a graph to a given situation (or vice versa). We need to translate a graph to a given situation (or vice versa).

Velocity Velocity is a vector that relates average displacement to average time. Velocity is a vector that relates average displacement to average time. Speed is the total distance divided by the total time for a trip. Speed is the total distance divided by the total time for a trip. For both, the formula is: For both, the formula is: v = ∆d ∆t ∆t

If you’re finding it from the graph, you are actually finding the slope of the section of line. If you’re finding it from the graph, you are actually finding the slope of the section of line. If you’re given numbers, simply plug them into the formula. If you’re given numbers, simply plug them into the formula. An easy way to manipulate the formula is to use the magic triangle: An easy way to manipulate the formula is to use the magic triangle: vt d

The units for the velocity or speed are just the units for distance slash the units for time. The units for the velocity or speed are just the units for distance slash the units for time. ex: Eiko skates to school, a total distance of 4.5 km. The journey takes her 0.62 hours. What is her average speed? v = d/t v = 4.5 km/0.62 h v = 7.3 km/h

Write down Newton’s 3 laws. Write down Newton’s 3 laws.

Try these… Graphing Distance vs Time Worksheet Graphing Distance vs Time Worksheet Graphing Speed vs Time Worksheet Graphing Speed vs Time Worksheet

Acceleration Acceleration - change in velocity per unit of time. Calculated as the slope of a straight line velocity-time graph Formula:a = Δv t Remember that Δv = final velocity – initial velocity!

ex: What’s the average acceleration of a rollercoaster that starts with an initial speed of 5 m/s but whose speed 4 seconds later is 25 m/s? a = v f – v i t = 25 – 5 4 = 20 4 = 5 m/s 2 **The units for acceleration are usually m/s 2 but watch out for time units that aren’t the same (change km/h to m/s before doing the questions!)**

Try these… Acceleration Worksheets Acceleration Worksheets

Newton’s Three Laws Newton came up with three laws that are very important for our study of science Newton came up with three laws that are very important for our study of science His first law was that an object in motion will stay in motion (or an object at rest will stay at rest) until acted upon by a force. His first law was that an object in motion will stay in motion (or an object at rest will stay at rest) until acted upon by a force. Also called… Law of Inertia Also called… Law of Inertia ex: A ball will keep rolling but only stops because the force of friction slows it and eventually stops it.

Newton’s second law states that a force Newton’s second law states that a force ( a push or a pull) that equals an object’s mass times it’s acceleration. This can be shown by f = ma This can be shown by f = ma The mass must be in kg and acceleration in m/s 2. The mass must be in kg and acceleration in m/s 2. The units for force are Newtons (N) The units for force are Newtons (N) ex: How much force will a 2 kg mass exert if it accelerates at 4 m/s 2 ? F = ma= (2kg)(4 m/s 2 )= 8N F ma

Newton’s third law is that for every action there is an equal and opposite reaction Newton’s third law is that for every action there is an equal and opposite reaction This is important in car collisions that we will look at later. This is important in car collisions that we will look at later. Newton’s three laws video Newton’s three laws video mnnDnKU mnnDnKU mnnDnKU mnnDnKU Bill Nye Bill Nye K3XZbc K3XZbc K3XZbc K3XZbc

Momentum Which causes a bigger dent in your car? A cyclist travelling at 50km/h or a tank travelling at 50 km/h? Which causes a bigger dent in your car? A cyclist travelling at 50km/h or a tank travelling at 50 km/h? Which would hurt you more? A bullet travelling at 1 m/s or one travelling at 30m/s? Which would hurt you more? A bullet travelling at 1 m/s or one travelling at 30m/s? Momentum depends on 2 factors, mass and velocity and therefore has the formula: Momentum depends on 2 factors, mass and velocity and therefore has the formula: p = mv

Mass must be in kg and the velocity is in m/s. Mass must be in kg and the velocity is in m/s. Therefore, the units for momentum is Therefore, the units for momentum is kg m/s The momentum of an object at rest is always zero The momentum of an object at rest is always zero There is a Law of Conservation of Momentum which means that the momentum before a collision equals the momentum after the collision There is a Law of Conservation of Momentum which means that the momentum before a collision equals the momentum after the collision

ex: How much momentum will a 500 kg truck travelling at 16.67m/s have? p = mv= (500)(16.67)= kg m/s If you have to change grams to kg, divide by 1000! p mv

Impulse Impulse - the impact of a force on a moving object over an interval of time. Impulse - the impact of a force on a moving object over an interval of time. Impulse changes the momentum of an object. It can make it larger or smaller. Impulse changes the momentum of an object. It can make it larger or smaller. It is a vector so it has direction It is a vector so it has direction It can be represented by the formula: It can be represented by the formula: I = Ft It will have the units Ns It will have the units Ns (Newton seconds) I Ft

Impulse can be increased in 2 ways: Impulse can be increased in 2 ways: 1) Increase the force being applied to change the object’s motion 2) Increase the time that the force is being applied for to change the object’s motion Which of the two above would be gentler? Which of the two above would be gentler?

Friction Friction is a resistive force exerted by a surface on a moving object Friction is a resistive force exerted by a surface on a moving object It is a force that opposes motion It is a force that opposes motion Generally, a rough surface will have greater friction and a smooth surface will have lesser friction. Generally, a rough surface will have greater friction and a smooth surface will have lesser friction. Friction has a great effect on the braking distances of cars Friction has a great effect on the braking distances of cars

There are 3 factors that effect the braking distance: There are 3 factors that effect the braking distance: 1) the velocity of the vehicle 2) friction (of the surface AND the brakes) 3) reaction time of the driver The mathematical formula for calculating braking distance on various surfaces is: The mathematical formula for calculating braking distance on various surfaces is: d = kv 2 where d is distance, k is a constant (table), and v is velocity in m/s

There are three situations that you may have to calculate the braking distance: There are three situations that you may have to calculate the braking distance: 1) Rubber tires on dry concrete (k = 0.06) 2) Rubber tires on wet concrete (k = 0.1) 3) Rubber tires on ice (k = 0.25) ex: What is the braking distance on dry concrete for a car travelling at 100km/h? 100km/h ÷ 3.6 = 27.8 m/s d = kv 2 = (0.06)(27.8) 2 = 46.3 m