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Exploration Physics 7. Perform a percent difference between your calculated centripetal acceleration and one given in the software. Discuss any differences. experiment theory guide exploration of physics A 8. Additionally, compute the linear speed by using the calculated "w" and the radius Procedure: input and then compare this to the one from the software. Note that the software lin speed can be simply calculated by using the equation, v = WR. D Investigating Period, centripeta acceleration and the component 9. Perform percent difference for the linear speed and discuss any differences. xy v. Vax ay velocity O Centripetal Force = ? N 10. Remember to perform at least 5 trials for the steps above. For each one of these tri Angular Velocity = ? rad/sec 1. Open "Exploration Physics" an you will change ALL VALUES, velocity, radius and mass. 0.0 seconds select Motion > > > Centripetal Fo: velocity (m/s) 20 radius (m) mass (kg) - 4.0 vector scaler 2.0 2. Run a couple of trials and obse Drawing the velocity vectors how the mass rotates at constant around the center. experiment theory guide exploration of physics 3. You will notice the vectors, the green vector which gives you the centripetal force a to the centripetal acceleration and the blue vector the linear speed. 4. You will create a table where you will have at least 5 trials for different values of rad xy v. V B. By mass and velocity and you will run the simulation that will give you: Centripetal fo Centripetal Force = 118.# N Angular Velocity = 0.63 rad/sec and angular velocity. 11.3 seconds velocity (mis) 50 radius (m) 5. Instead of using the angular velocity given in the software, compute it by using mass (kg) vector scaler 1.0 equation: w = 2pi Where T = period. You will measure this period by reading the t of one period of the trajectory (one whole circumference). 6. Using this value, compute the centripetal acceleration by using, F. = m * w2 * R1. Reset the simulation and choose a suitable value for the centripetal force. You will the simulation to keep this value constant. 2. For at least 4 trials, adjust the values of mass and radius BUT keep the velocity const 3. Build a table of values making sure that for each trial you annotate the value of centripetal force you adjusted and the velocity. 1. Reset the simulation and run different trials until you get a speed you feel comfort 4. Remember that according to the equation if you increase the mass, you must incre with (it should be a value where you can stop and observe the velocity vectors). the radius to keep the force constant. 2. Make sure the vector scalar is 1.0 5. Plot Mass vs Radius in the XY plane and fit a line through the points. What does slope represent? 3. Choose a suitable value for the centripetal acceleration such that you can clearly : the angle between the green vector force and the "x" axis. 6. If you can find another suitable value for the centripetal force, repeat the steps above, otherwise, include your graph, your table and your calculations for slope 4. Pause the simulation and use geometry and trigonometry to find the angle between and comparisons. velocity vector and the horizontal axis. 5. Use this angle to compute the Vxand Vy values. How do they compare to the one the table? ( You will not be able to compare them numerically BUT you will be abl Questions: compare them by the proportion between them) 1. Which section of the lab allowed you to understand the relationship between 6. Draw a sample diagram. period of rotation and centripetal force? 7. You will only doe ONE trial for this procedure. 2. Using the graph from the last section, what can you conclude from the relationship between mass and radius in a constant rotational motion (if the force is fixed)? Further investigation of F. = m + R\fPHYSICS 111 Experiment # Circular Motion and In the case of a circular path the radial direction is always In the static method, a hanging mass is used to stretch the spring to Centripetal Force normal to the tangent line, andtherefore the acceleration radius R of a mass performing UCM is always inward along a The static calculation to stretch the spring is spring = Mhanging9 Name: Grade: radius toward the center of the circle. The magnitude of the acceleration can be shown to be The 2nd verification of Newton's 2nd Law for a mass performing Instructor: Partners: aucm = V2 where "v" is the speed and "R" is the radius of the circle. UCM is to show there is an inversely proportional relation between mass and velocity squared, provided the radius and force are held Date Performed: Comments: The time for the mass to go once around the circle is calledthe period constant, Fc = m - and V2 = (FR)M-1 Date Submitted: and denoted by the Greek letter tau, T . In a time " I " the mass will travel a distance equal to the circumference of the circle, 2ntR In our experiment the centripetal force (provided by the spring ) varies Objective: We there for have V = Distance 2nR only with the radius; thusly when the radius is held constant, then time centripetal force is constant. From the experimentally determined To determine how centripetal force is a function of rotating mass and Since the object is accelerating there must be a net nonzero force periods at a fixed radius, a Vz vs. m graph should give an equation the radius of rotation and to compare calculated and measured values acting on the mass. By Newton's 2nd law the direction of the net for a power fit trend line with a exponent of -1 and a coefficient of of centripetal force. force is also along a radius inward toward the center of the circle. The value Fc R. net force acting on a mass performing UCM is called the Centripetal Theory: V 2 force. Centripetal is from the Greek meaning "center seeking." The Proof aUCM R centripetal force is not a physical force like gravity, or a tension but A mass moving in a circular path with constant speed is performing is the name given to the net force causing UCM. The name reminds Vidirection In uniform circular motion the magnitudes of the Uniform Circular Motion (UCM). position vectors are equal |rf = In) = R and the us the net force for UCM is inward along a radius of the circle. The magnitudes of the velocity vectors are equal | Vil = [Vil UCM is an example of accelerated motion where only the direction 2nd law also tells us the magnitude of the net force is Fc = m =V . As a consequence of the path being circular, the of the velocity is changing. The magnitude of the velocity (speed) position vector (radial) must be normal to the velocity vector (tangential). By looking at the right triangle remains constant. Method of Investigation: with angle 0, we can write (90 - 0) + 90 + y = 180 Quite generally if an acceleration is to only change the direction of In our experiment the Centripetal Force is provided by the stretched From this we obtain = V. The triangles formed by the position spring. The first verification of Newton's 2nd Law for a mass AV the velocity, the acceleration must be perpendicular to the direction vectors and velocity vectors are similar and we can write V = R of the velocity, i.e. the acceleration must be normal to the tangent performing UCM is to determine the force necessary to stretch the line to the path. spring a specified distance in two different ways ( dynamically and AV V Ar by a static method) and compare the results. The average acceleration is dave = At R At Uniform Circular Motion (UCM) The dynamic method experimentally determines the period of the In the lim it as At - 0, # = V and aUcm = mass performing UCM in a circle of radius "R" and uses the period V 2 Required Equipment: to calculate the centripetal force, Fc = Fspring = M- = m- 4TT- R T2 Exploration Physics