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HOW TO SOLVE KINEMATICS PROBLEMS To solve problems involving straight line motion with constant acceleration it is important to clearly identify what is known and what we are looking for and choose which of 4 main formulas to use. 1. If you know initial velocity, acceleration, time and looking for final velocity, if you know initial velocity, acceleration, final velocity and looking for time, if you know initial velocity, time, final velocity and looking for acceleration, if you know time, acceleration, final velocity and looking for initial velocity use formula 2. If you know initial velocity, acceleration, final velocity and looking for displacement, if you know initial velocity, acceleration, displacement and looking for final velocity, if you know initial velocity, final velocity, displacement and looking for acceleration, if you know acceleration, displacement, final velocity and looking for initial velocity use formula 3. If you know initial velocity, time, displacement and looking for final velocity, if you know initial velocity, final velocity, displacement and looking for time, If you know initial velocity, time, final velocity and looking for displacement, If you know final velocity, time, displacement and looking for initial velocity use formula 4. If you know initial velocity, time, displacement and looking for acceleration, if you know initial velocity, time, acceleration and looking for displacement, if you know initial velocity, displacement, acceleration and looking for time, if you know displacement, time, acceleration and looking for initial velocity use formula Yuriy Verkhatsky 5. If you have 2 unknown in the formula that you want to use – use another formula according to abovementioned steps to find one of the unknown. 6. Remember that if problem involves object thrown vertically up – it’s velocity at the highest point is 0. If object starts from rest or dropped – it’s initial velocity is 0. 7. If problem involves 2 moving objects meeting each other, than you need to write down equation of the motion for each object taking in the account initial positions (as origin you should take position of one of the objects and axis along line of motion) and at what time each object started to move (can be not at the same time!) and solve equation. Yuriy Verkhatsky equalize positions HOW TO SOLVE DYNAMICS PROBLEMS 1. Sketch the diagram. 2. Label all forces acting on the object (objects) of interest. If there objects connected with the string (rope etc.) there will be 2 same tension forces along the string directed away from each object. 3. Choose axis. If incline plane involved, choose one axis along the plain, one perpendicular to plane. There is one exclusion – for problems involving circular motion on the banked road choose one axis horizontally, another vertically. Feel free to choose positive direction of the axis: up, down, left, right, whatever is more convenient. Usually better choice will be in the direction of the acceleration. 4. Write down second Newton’s law in resolution into chosen axis. ∑
Make sure that you will include all forces. If resolution of the force is in the positive direction of the axis it will be positive in your equation, if in the opposite direction then negative. Same for the acceleration on the right hand sign. Make sure that you apply trigonometry properly, if resolving into the adjacent axis use cos, if into opposite, use sin. If problem involves connected objects, write 2nd Newton’s law for each object separately. If problem involves circular motion with the constant speed, acceleration will be always directed towards centre of the circle. 5. Do math to find unknown quantities. Yuriy Verkhatsky HOW TO SOLVE COLLISION PROBLEMS 1. Choose axis. 2. Identify initial (before collision) momentum of each object involved in resolution into the chosen axis (i.e. positive or negative). 3. Identify final (after collision) momentum of each object involved in resolution into the chosen axis. If objects stick together after collision treat them as one object with the mass equal sum of the masses of objects involved. 4. Equalise sum of the initial momentum of object involved to the sum of the final momentum (taking in the account positive or negative sign according to resolution into axis). 5. Do math to solve equations and find unknown quantities. If question asking about impulse or force, use equation ∆
∆ Remember to use change of momentum of the single object and calculate change of momentum as final minus initial in resolution in chosen axis. 6. To find out is collision elastic or inelastic, calculate initial total kinetic energy (sum of kinetic energy of all objects involved before collision) and final total kinetic energy. If they are equal collision is elastic, if not – inelastic. By the way, if objects stick together after collision, it always inelastic. Yuriy Verkhatsky HOW TO SOLVE PROJECTILE PROBLEMS 1. Chose origin and axis. Usually the best choice will be to chose x=0 on the vertical line passing through launch point and y=0 either at launch point or at the end point level, whichever is lower. x axis directed usually to the right and y axis up. 2. Identify resolution of the initial velocity into chosen axis. cos sin In case of horisontal launch and 0 In rare case of launch direction below horisontal line, angle has to be taken as negative. 3. Write down equations of the motion along each axis. Motion in horisontal direction is with the constant speed so equation is , where is initial x position, usually 0. Motion in vertical direction is with the uniform acceleration g=10 m
equation is down so 5 4. Sub all known values in those equations. Instead of x and y sub in final position, often for y it will be 0. Solve obtained simultaneous equations and find unknown values. 5. If you need to find final velocity use formula to find speed (magnitude of velocity), where and are final components of velocity. and Yuriy Verkhatsky 10 To find angle θ with the horisontal use formula tan
6. In case when launch point is at the same level as end point you can use standard formulas for maximum height H and range L: and Final speed in this case equal to initial and final angle equal initial with minus (as angle below horisontal) . Yuriy Verkhatsky HOW TO SOLVE PROBLEMS INVOLVING LENZ’S LAW 1. Identify direction of the external magnetic field. 2. Identify what happens to the flux created by external field – does it increasing or decreasing. 3. If external flux decreasing – induced magnetic field will be in the same direction as external magnetic field. 4. If external flux increasing – induced magnetic field will be in the opposite direction to external magnetic field. 5. After identifying direction of induced magnetic field use right hand grip rule (or screwdriver rule) to identify direction of induced current. Yuriy Verkhatsky HOW TO SOLVE PROBLEMS INVOLVING THERMISTOR OR PHOTODIODE (LDR) IN CONTROL CIRCUITS 1. With increase of temperature resistance of the thermistor decrease. As resistance of thermistor decrease, more voltage drop will be across resistor R and less across thermistor. So to switch on cooling (we switching cooling on when temperature increase) voltage output must be taken from resistor as it increases when temperature rise. 2. With decrease of temperature resistance of the thermistor increase. As resistance of thermistor increase, more voltage drop will be across thermistor and less across resistor R. So to switch on heating (we switching heating on when temperature decrease) voltage output must be taken from thermistor as it increases when temperature drop. 3. With decrease of illumination resistance of the LDR (photodiode) increase, so more voltage will be across LDR (photodiode). So to switch on illumination when it becomes too dark, voltage output must be taken from LDR (photodiode). 4. Identify resistance of thermistor (LDR) from given graph based on given temperature or illumination, use Ohm’s law to find current through voltage divider when voltage equal required for switching on device. In case of photodiode you will find current directly from given graph. Then voltage across variable resistor equal voltage supplied minus voltage across thermistor (LDR). Use Ohm’s law again Yuriy Verkhatsky to find required value of variable resistor.