Forces and Motion Notes (APF)

# Vector and Scalar Quantities Some things we measure have a direction as well as an amount. These are called **vector quantities**. Some things we measure only have an amount. These are called **scalar quantities**. Complete the following circus of experiments answering the questions as you go. #...

# Vector and Scalar Quantities Some things we measure have a direction as well as an amount. These are called **vector quantities**. Some things we measure only have an amount. These are called **scalar quantities**. Complete the following circus of experiments answering the questions as you go. ## Beaker of Water - What is the temperature of the water? 21℃ - Is temperature a vector or scalar? **scalar** ## Tennis Ball - Gently throw the tennis ball in the air. - What is the force that makes the ball go up? **Hand** - What is the force that brings it back down? **Gravity** - Is force a vector or scalar? **vector** ## A Bit of Exercise - How long does it take for you to do ten starjumps? 7.415 - Is time a vector or scalar? **scalar** ## A Thumbprint - Press your thumb into the blue tac to make a thumbprint. - Is pressure a vector or scalar? **vector** ## Crooke's Radiometer - Turn the light on and observe what happens? - Is light scalar or vector? **scalar** # APF Wednesday 1th September 2024 ## Distance and Displacement - **Distance** is how far an object actually moved. - Distance does not involve direction. - **Displacement** is the distance an object has moved in a straight line. It has both magnitude and direction. ### Consider a running track. - 100m race = distance: 100m, displacement: 100m - 400m race = distance: 400m, displacement: 0m # APF Forces - A force is a push or a pull that acts on an object. Force is measured in Newtons. ## Contact and Non-Contact forces - With a contact force, the two objects have to touch. | Contact | Non-Contact | |---|---| | Air resistance | Gravity | | Friction | Magnetic | | Drag | Thrust | | Elastic | Electrostatic | | Normal Contact | Strong Nuclear | | Upthrust | Weak Nuclear | | Tension | | Thrust | | Compression | | Lift | # Prep 5.1.1 Scalar and Vector Quantities 1. What is the difference between a Scalar quantity and a Vector quantity? *Scalar quantities have magnitude, while vector quantities have magnitude and direction* 2. Make a list of some scalar quantities. *Time, temperature, speed, distance, mass, volume, density, pressure, energy, work, power* 3. Make a list of some vector quantities. *Force, pressure, velocity, acceleration, displacement, momentum, impulse* 4. Use a piece of string and a rule to find the distance travelled in each of the following journeys. Use a rule to find the displacement for each of the journeys. 1cm = 1m - [Image describing journey A-E with distances and journey time] - [Image describing journey H-L with distances and journey time] - [Image describing journey B-J with distances and journey time] 5. For each of the journeys above, calculate the speed. 6. For each of the journeys above, calculate the velocity. 7. A BMX cyclist completes 1 circuit of a 1km at a constant speed. - If she completes 1 circuit in 50 seconds, calculate her speed. - Explain why her velocity is not constant. 8. The moon orbits the Earth at a constant speed but not a constant velocity. Explain this statement. # APF Friday 13th September 2024 ## Resultant Forces - The resultant force on an object is the overall force when all the forces acting are taken into account. ## Drawing Forces - We draw forces with an arrow. The length of the arrow indicates the magnitude (size). The direction of the arrow shows the direction of the force. - [Image of 2N arrow + 4N arrow] ## Calculating resultant forces in a straight line - If the forces act in the same direction, add them. - [Image of 30N arrow + 10N arrow] -> F_resultant = 30 + 10 = 40N - If the forces act in opposite directions, subtract them. - [Image of 500N arrow - 200N arrow] -> F_resultant = 500 - 200 = 300N ## Remember - Force is a vector quantity so you must include both the magnitude and direction. # Resultant Forces and motion - If the resultant force and the motion are in the same direction, the object will accelerate. - If the resultant force and the motion are in different directions, the object will decelerate. - [Image of car going at constant velocity] - [Image of car decelerating] - [Image of car accelerating] # APF Wednesday 18th September 2024 ## Weight & Mass - Weight and mass are different. Mass is the measure of the amount of matter in an object. - Your **mass** doesn't change if you're on a different planet. - **Weight** is a force due to the pull of gravity (N). ## Equation for weight - W = M x g - W = weight in N - M = mass in kg - g = gravitational field strength in N/kg. - On Earth, g = 9.81 N/kg # Prep ## Balanced Forces - Copy and complete the following: - The total forces acting to the right add up to 47 Newtons. - The total forces acting to the left add up to 47 Newtons. - The two forces are exactly the same size and so the overall effect of the forces is **ZERO** Newton's. - When the overall effect of the forces is ZERO, then we say that the forces are **balanced** and there is **NO RESULTANT FORCE**. ## Unbalanced Forces - Copy each diagram and: - Calculate the resultant force. - State the direction of motion. - Draw an arrow representing the resultant force vector. - [Image of Diagram a] - [Image of Diagram b] - [Image of Diagram c] - [Image of Diagram d] - [Image of Diagram e] - When this happens: - A stationary object will not move. - A moving object will continue at a constant speed. ## Diagrams with no resultant forces. - Copy the diagrams and find the size of forces A to I. Show your working. - [Image of forces A-I] # APF Friday 13th September 2024 ## TASK - A journey around the Solar System First measure your own mass using the scales provided in class (use 55kg) and then calculate your weight on each planet. | Planet | Acceleration due to gravity (m/s²) | Mass (kg) | Weight (N) | |---|---|---|---| | Mercury | 3.61 | 55 | 198 | | Venus | 8.83 | 55 | 485.65 | | Earth | 9.81 | 55 | 539.55 | | Mars | 3.75 | 55 | 206.25 | | Jupiter | 26.0 | 55 | 1430 | | Saturn | 11.2 | 55 | 616 | | Uranus | 10.5 | 55 | 577.5 | | Neptune | 13.3 | 55 | 731.5 | | Pluto (dwarf planet) | 0.61 | 55 | 33.55 | # APF Wednesday 25th September 2024 ## Parallelogram of Forces - We know how to calculate a resultant force if the forces are in a straight line. But what about if they are at an angle? ## Right Angles - We draw a scale diagram, ie: one where the length of the line is scaled to the magnitude of the force. - **Scale = 10N: 1cm** - [Image of 10N arrow + 50N arrow and parallelogram] To calculate the resultant force, we: 1. Complete the parallelogram. 2. Draw starting corner (O) & finishing corner (O) 3. Add direction. (1) 4. Measure the length of the resultant force (6.4cm) 5. Using the scale, calculate the force. - F = 64N - θ = 38° - It may not be at right angles, but you still use a scale diagram. ## All other angles - **Scale = 1N: 1cm** - [Image of 8N arrow + 6N arrow and parallelogram] To calculate the resultant force, we: 1. Complete the parallelogram. 2. Draw starting corner to finishing corner 3. Add direction (1) 4. Measure the length of the resultant force (12.2cm) 5. Using the Scale, calculate the force. - F = 12.2 N - θ = 25° # Draw scale diagrams (1cm = 1N) to work out the Resultant force in each of these cases: - [Image of example 1] - [Image of example 2] - [Image of example 3] - [Image of example 4] - [Image of example 5] - [Image of example 6] - [Image of example 7] - [Image of example 8] - [Image of example 9] - [Image of example 10] - Calculate the resultant force (using a scale diagram) for the following scenarios. - [Image of Parallelogram 1] - [Image of Parallelogram 2] - [Image of Parallelogram 3] - [Image of Parallelogram 4] - [Image of Parallelogram 5] # APF Wednesday 2nd October 2024 ## Force and Elasticity - When a force acts on an object, one of 3 things can happen: - It can change speed. - It can change direction. - It can change shape. ## Changing Shape - To change the shape, we either use compression or tension. - Both these forces will produce an extension in the material. The amount of extension produced depends on: - The force that has been exerted on the object. - How easily the object changes shape. ## Spring Constant - This is a value which indicates how easily a spring can be stretched. The spring constant of an object, k, is the number of Newtons (ie: the force required to stretch the object by 1m). - **Equation linking F, k, and extension** - F = k x e - k = F/e - e = F/k - F = force in N. - k = spring constant in N/cm or N/m. - e = extension in m or cm. ## Example - A spring is 0.36m long. When it's pulled by a force of 2N, it stretches to 0.42N. What is its spring constant? Assume the spring behaves elastically. - k = Force / extension - k = 2 / 0.04 - k = 50 N/m # APF Friday 4th October 2024 ## 4.5.3 Force and extension Practical - It is easy to make a spring by winding a length of wire around a cylindrical object. You can investigate how springs behave when loaded with a weight. You are going to investigate the relationship between the force applied to stretch a spring and its extension. ### Learning outcomes - Accurately measure the extension of a spring to calculate the spring constant. - Plot a graph of results and identify the limit of proportionality. ### Maths Skills Required - Plot two variables from experimental data. - Interpret graphs that represent a linear relationship. - Calculate the gradient of a graph. ### Formula - Force = spring constant x extension. - F = k e ### Apparatus list - spring - set of masses and mass holder appropriate for the spring you are testing. - clamp stand - ruler - 1kg mass to put on base of clamp stand to stabilize it OR a table clamp. - eye protection ### Safety notes - Be careful not to drop the masses on to your foot. ### Common mistakes - Don't confuse length with extension. The extension is the stretched length minus the original length of the spring. - Try not to stretch the spring when you add and remove masses. ### Method 1. Set up the equipment as shown in Figure 1, but without any masses or the mass holder on the spring. 2. Measure the length of the spring with no masses attached. Record this length in Table 1 in the Length of spring (cm) column for 0 N. The extension is filled in for you: no force means no extension. 3. Add a mass holder to the end of the spring and measure the length of the spring, using the pointer to improve accuracy. 4. Record the force on the spring and the new length of the spring in Table 1; a mass of 100g has a weight of 1N. Calculate how much the spring has extended: new length - original length for 0 N. ### Figure 1 - [Image of a spring with a mass attached] - [Image of a graph with an anomalous result] ### Check your understanding 1. Look at the graph and describe the relationship between force and extension. *Force and extension are almost directly proportional.* 2. Identify the limit of proportionality on your graph. *2N* # APF Wednesday 9th October 2024 ## Analysis of spring constant (Practical) - The graph of extension against force is a straight line through the origin. This graph is directly proportional. - To calculate the spring constant K, you pick a force (F) and find the corresponding extension (e) - [Image of a spring with a force applied] - (P is the limit of proportionality) if a spring is stretched beyond this point, it will not return to its original shape. ### Accuracy & Safety - To make sure that the experiment was safe, we wore safety goggles in case the spring "pinged" off into our eyes, and we G-clamped the equipment to the desk so it did not topple over. - To make sure that the experiment was accurate, we made sure that the ruler was close to the spring, and we used a pen to color as a marker to read the correct measurement on the ruler. We also ensured that we were reading at eye-level to avoid parallax errors. # APF Wednesday 9th October ## Comparing Different Springs - [Image of Graph a and Graph b] - Spring A is stiffer as it needs 4N of force to stretch it 2cm, whereas B only needs 2N to stretch the same amount. ## Centre of mass & stability - The centre of mass of an object is where the weight of an object may be considered to act at a single point. For anything symmetrical, that is the centre. # APF Wednesday 16th October 2024 ## Speed & Velocity - Speed is a scalar quantity. - Velocity is a vector quantity. - A = 60m/20s = Distance - A = 40m/20s = Displacement - Average speed = Distance / Time = 60/20 = 3 m/s - Average velocity = Displacement / Time = 40/20 = 2 m/s ## Relative velocity - Consider Train A moving to the right. - A = 25m/s = velocity = V_A - If train B moves to the left, we say that its velocity is negative. - B = -25m/s = V_B ## Average Speed Calculations - Typical Speeds: - See ppt and learn. - Average Speed of Mars: - Distance = 2πr = 2 x π x 220 x 10^6 x 10^3 m. - Average Speed = Distance / Time = (2 x π x 220 x 10^6 x 10^3) / 687 x 24 x 60 x 60 = 2.33 x 10^4 m/s # Distance Time graphs - **Stationary:** - [Image of a stationary graph] - **Constant velocity:** - [Image of a constant velocity graph] - A is slower. - B is faster. - Velocity = Gradient. - **Accelerating:** - [Image of an accelerating graph] - **Decelerating:** - [Image of a decelerating graph] - **Do these please:** - [Image of exercises] # Prep ## Acceleration - 10 / 5 = 2 m/s^2 - 4 / 8 = 4 m/s^2 - 15 / 50 = 0.3 m/s^2 - 9 - 10 / 2 = -0.5 m/s^2 - 4 / 5 = 0.8 m/s^2 - 14 / 5 x 7/8 = 9.1 m/s^2 ## Change in acceleration - Change = acc x time - 10.5 / 7/20 = 0.510 - Final = Change + Initial - 10 + 16 = 16m/s x 11m/s - Change = acc x time - 50 x 30 = 150 - Final = Change + Initial - 150 + 100 = 250m/s x 1600m/s - Change = a x t - 30 x 5 = 30 - Initial = 30 + 30 = 50m/s 0m/s - Change = a x t - 3 x 4 = 12 - Initial = 12 + 18 = 6m/s - Time = change/ace - 20 / 2 = 10m/s - Time = 24/2 = 12m/s - acc = (v_f - v_i) / t - (840010 - 25) / 50 - -15/ 50 = -0.3 - Change = acc x time - -3 x 2 = -6 - Final = Change + Initial - -6 + 10 = 6m/s x 4m/s - Mrs Jauncey has seen my work. ## Q2 - (i) F = E - (i) B - C, D - E - speed = 750m / 100s = 7.5m/s - 445 and 250m / 5.67 m/s # APF Wednesday 6th November 2024 ## Calculating velocity from a distance-time graph ### Distance(m) - **Velocity (speed) = gradient of a distance-time graph.** - Velocity at 2s (when the line is straight) use gradient. - V = 4 / 1 = 5m/s ### Velocity at 5s (when the line is curved) - Use the gradient by drawing a tangent. ### Velocity Time graphs - **Stationary:** - **Constant velocity:** - [Image of constant velocity graph] - B is faster. - **Constant acceleration:** - a = (v_f - v_i) / t - Gradient = Acceleration. - **Constant deceleration:** - [Image of constant deceleration graph] - **Combined d-t and v-t graphs:** - [Image of Combined graph] # APF Friday 8th November 2024 ## Velocity time graphs - Calculating the distance travelled from a velocity-time graph. - We calculate the distance travelled using the equation distance = velocity x time. - Consider an object moving at constant velocity. - Distance = average velocity x time. - [Image of constant velocity graph] - Now consider an object that is accelerating. - Distance = average velocity x time. - [Image of accelerating graph] # AQA Physics GCSE Student activity - **Look at the velocity-time graph of a motorbike and then answer the questions.** - [Image of motorbike graph] - **Calculate the acceleration of the motorbike during this time. Show your calculations.** - a = (v_f - v_i) / t = (15 - 0) / 10 = 1.5m/s^2 - **This question is about parts of the graph showing the motorbike going at constant velocity.** - **For how long does the motorbike travel at a constant velocity?** 30s - **At what velocities does this happen?** 15m/s and 25m/s - **Complete the graph showing that at 80 seconds, the motorbike remains at rest for 10 seconds.** - [Image of extended graph] - **This question is about the acceleration of the motorbike** - **What velocity does the motorbike reach in the first 5 seconds?** 7m/s - **Between what times does the motorbike travel at its highest velocity?** 40-60s. - **When is the motorbike's velocity changing at its greatest rate? Explain your answer.** It decelerates as it changes speed by -25 in 7s, between 0-10s. - **What is the acceleration of the motorbike between 20 and 40s? Show your calculations.** a = (v_f - v_i) / t = (25 - 15) / 20 = 0.5m/s^2 - **This question is about the distance travelled by the motorbike. Work out the distance travelled by the motorbike between 40 and 80 seconds. Show your working.** - (500 + 250) = 750m # APF Wednesday 8th November 2024 ## Terminal Velocity - For explanation of parachutists, see p.p.t - **Q1.** - When a car is driven efficiently the engine gives a constant forward pull as the car accelerates to its maximum speed. During this time frictional forces and air resistance oppose the forward motion of the cart. The sketch graphs below show how the car's speed increases when only the driver is in the car, and when the driver has a passenger in the car. - [Image of speed v time graph] - **How does the acceleration of the car change with time?** It decreases. - **What conclusion can be made about the resultant (net) forward force on the car as its speed increases?** The net force becomes 0 and then decreases. - **On the graph, draw a line to show how you would expect the car's speed to vary if it carried three passengers.** - **The manufacturer of a family car gave the following information:** - Mass of car 950kg - The car will accelerate from 0 to 33 m/s in 11 seconds. # Equation linking Resultant Force, Mass and Acceleration - F = ma - F = Resultant Force. - m = mass in kg. - a = acceleration in m/s^2 # APF Friday 22nd November 2024 ## Moments & Levers - **Moments** - The size of a moment depends on: - The size of the applied force. - The perpendicular distance from a pivot that the force is applied. - M = F x d - M = moment - F = force - d = distance - M = Nm - F x d = N - d = m ## Investigating moments. - [Image of lever with masses] ## A Lever - A lever is a simple machine that makes work easier to do. For example, scissors, or opening a door. ## You must show your working. You were losing too many marks because you are not thinking carefully. ## Review Questions - Moments 1. a) Explain how a turning effect could be increased without increasing the force. *Move the force further perpendicularly away from the pivot* 1. b) Explain how a moment could be increased without changing the position of the applied load from the pivot. *Increase the force.* 2. Complete the table below. | Force (N) | Distance (m) | Moment (Nm) | |---|---|---| | 10 | 0.15 | 1.5 | | 50 | 0.5 | 25 | | 100 | 0.8 | 80 | | 80 | 1 | 80 | | 125 | 1.2 | 150 | 3. A rusted bolt requires a turning effect of 120 Nm to turn and a wrench providing 0.4 m force application from the pivot is used. How much force is required? *120 / 0.4 = 300N* 4. A force of 30N is applied 15cm away from the pivot, what is the moment produced? *30 x 0.15 = 4.5 Nm* 5. A force of 0.1 kN is applied 20 cm away from the pivot, what is the moment produced? *0.1 x 0.2 = 0.02 kNm* # APF Wednesday 27th November 2024 ## Balancing Moments - If something is balanced, then the sum of the clockwise moments is equal to the sum of the anti-clockwise moments. - [Image of balanced lever] - (F2 x d1) + (F1 x d2) = (F3 x d3) ## Centre of Gravity: SO.95cm | Weight of Mass in Newtons | Distance p (mm) | Distance q (mm) | q/W (mm/N) | |---|---|---|---| | 100N | 275 | 220 | 220 | | 2N | 190 | 305 | 152.5 | | 2N | 148 | 347 | 115.6 | | 4N | 120 | 375 | 93.75 | | 5N | 102 | 393 | 78.6 | - [Image of graph q/W vs Distance P] - **Calculations:** - When the ruler is balanced the anticlockwise moment caused by the weight of the masses is equal to the clockwise moment caused by the weight of the ruler. - Therefore: - weight of mass, W (N) x distance p (mm) = ruler weight R (N) x distance q (mm) - Calculate the value distance q divided by weight of mass, W [q/W] for each of your results in the appropriate column in the table. - Draw a graph of distance p (mm) [Y-AXIS] against q / W (mm/N) [X-AXIS] - Measure the gradient of this graph. - The gradient is equal to the weight of the ruler in newtons. - Write out clearly your answer. - Explain why the gradient of your graph equals the weight of the ruler. # Friday 24th November 2024 ## Moments and Levers - **Q1.** - A camera boom is used at a television studio to allow filming from different positions. Figure 1 shows the arm of the boom in three different positions. - [Image of a camera arm] - In which position will the weight of the camera cause the largest moment about the pivot? *A*. - Give the reason for your answer. *Perpendicular distance is biggest.* - Complete the sentence. *Choose the answer from the box. When the moment caused by the weight of the camera increases, the moment caused by the counterweight increases.* - The camera has a mass of 5.0 kg. Gravitational field strength = 9.8 N/kg. Calculate the weight of the camera. *W = mg = 5 x 9.8 = 49N* # APF Prep - due 4/12/24 1. Niels Bohr, Ernest Rutherford + Niels Bohr 2. Niels Bohr + JJ Thompson 3. Ernest Rutherford 4. James Chadwick - 50% # Atomic Structure Timeline - 450 BC Greek philosopher Democritus suggests atoms for the first time. - 1803 John Dalton suggests solid spheres. - 1897 JJ Thompson discovers electrons and suggests the plum pudding model. - 1909 Geiger and Marsden did the alpha scattering experiment. - 1911 Ernest Rutherford put forward the nuclear model. - 1913 Rutherford and Niels Bohr refined the nuclear model to having electrons in shell rather than just outside the nucleus. - 1932 James Chadwick discovers an uncharged particle in the nucleus which he calls the neutron.