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Questions: 5. Use this angle to compute the Vand Vy values. Howdo they com to the ones in the table? (You will not be able to compare t 1. Which section of the lab allowed you to understand the numerically BUT you will be able to compare them by the propo: relationship between period of rotation and centripetalforce? between them ) 6. Draw a sample diagram. 2. Using the graph from the last section, what can you conclude from the relationship between mass and radius in a constant 7. You will only doe ONE trial for this procedure. rotational motion (if the force is fixed)? Further investigation of F = m * R 3. Discuss what is being demonstrated in this experiment. 1. Reset the simulation and choose a suitable value for the centri force. You will use the simulation to keep this value constant. End of document 2. For at least 4 trials, adjust the values of mass and radius BUT : the velocity constant. 3. Build a table of values making sure that for each trial you ann the value of the centripetal force you adjusted and the velocity 4. Remember that according to the equation if you increase the n you must increase the radius to keep the force constant 5. Plot Mass vs Radius in the XY plane and fit a line through the pc What does the slope represent? 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 and comparisons.In the lim it as At - 0, guide , At = Vand aUCM = this period by reading the time of one period of the trajectory Required Equipment: whole circumference). A Exploration Physics 6. Using this value, compute the centripetal acceleration by using, m * wz * R experiment theory guide exploration of physics 7. Perform a percent difference between your calculated centrij Centripetal Force = 118 8 N Angular Velecity = 0.63 radhee A acceleration and the one given in the software. Discuss any 11.3 seconds differences. whocity gong 50 Procedure: mass (ego Investigating Per 8. Additionally, compute the linear speed by using the calculated xy v. va, a and the radius you input and then compare this to the one from centripetal software. Note that the software linear speed can be simply calcu Centripetal Force = ? N acceleration and Angular Velocity = ? radisec by using the equation, v = WR. 0.0 seconds components of velocity velocity (m's) 20 radius (m) 9. Perform percent difference for the linear speed and discuss any mass (g) 40 vector scaler 20 differences. 1. Open "Exploral D Physics" and seler 10. Remember to perform at least 3 trials for the steps above. For Motion > > > Centripetal Force. one of these trials, you will change ALL VALUES, velocity, re and mass. 2. Run a couple of trials and observe how the mass rotates at con rate around the center. Drawing the velocity vectors 1. Reset the simulation and run different trials until you get a speed 3. You will notice the vectors, the green vector which gives you feel comfortable with (it should be a value where you can stop observe the velocity vectors). centripetal force align to the centripetal acceleration and the vector the linear speed. 2. Make sure the vector scalar is 1.0 4. You will create a table where you will have at least 5 trials for diffi 3. Choose a suitable value for the centripetal acceleration such that values of radius, mass and velocity and you will run the simul; that will give you: Centripetal force and angular velocity. can clearly find the angle between the green vector force and "x" axis. 5. Instead of using the angular velocity given in the software, comp 2pi 4. Pause the simulation and use geometry and trigonometry to fin by using the equation: w = 7 : where T=period. You will mea angle between the velocity vector and the horizontal axis.PHYSICS 111 Experiment # Circular Motion and In the case of a circularpath the radial direction is always to calculate the centripetal force, Fc = Fspring = m =m 472 R Centripetal Force normal to the tangent line, and therefore the acceleration 72 of a mass performing UCM is always inward along a Name: Grade: radius toward the center of the circle. In the static method, a hanging mass is used to stretch the spring to The magnitude of the acceleration can be shown to be radius R. Instructor: Partners: V 2 The static calculation to stretch the spring is spring = Mhanging9 aucm = where "v" is the speed and "R" is the radius of the circle. Date Performed: Comments: The 2nd verification of Newton's 2nd Law for a mass performing The time for the mass to go once around the circle is calledthe period UCM is to show there is an inversely proportional relation between Date Submitted: and denoted by the Greek letter tau, T . In a time " I " the mass mass and velocity squared, provided the radius and force are held will travel a distance equal to the circumference of the circle, 2ntR Objective: We there for have V = - Distance constant, Fc = m - and V2 = (FOR)M-1 time In our experiment the centripetal force (provided by the spring) varies To determine how centripetal force is a function of rotating mass and Since the object is accelerating there must be a net nonzero force only with the radius; thusly when the radius is held constant, then 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 centripetal force is constant. From the experimentally determined of centripetal force. force is also along a radius inward toward the center of the circle. The periods at a fixedradius, a V vs. m graph should give an equation net force acting on a mass performing UCM is called the Centripetal for a power fit trend line with a exponent of -1 and a coefficient of Theory: force. Centripetal is from the Greek meaning "center seeking." The value Fo 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 V 2 Uniform Circular Motion (UCM). us the net force for UCM is inward along a radius of the circle. The Proof aUCM 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 - Vidirection In uniform circular motion the magnitudes of the position vectors are equal |rf = In| = R and the of the velocity is changing. The magnitude of the velocity (speed) magnitudes of the velocity vectors are equal | Vil = [Vil remains constant. Method of Investigation: = V. As a consequence of the path being circular, the position vector (radial) must be normal to the velocity Quite generally if an acceleration is to only change the direction of In our experiment the Centripetal Force is provided by the stretched vector (tangential). By looking at the right triangle the velocity, the acceleration must be perpendicular to the direction spring. The first verification of Newton's 2nd Law for a mass with angle 0, we can write (90 - 0) + 90 + y = 180 of the velocity, i.e. the acceleration must be normal to the tangent performing UCM is to determine the force necessary to stretch the . From this we obtain 0 = V. The triangles formed by the position line to the path. spring a specified distance in two different ways ( dynamically and AV Ar by a static method) and compare the results. vectors and velocity vectors are similar and we can write V = R Uniform Circular Motion (UCM) The dynamic method experimentally determines the period of the AV V Ar The average acceleration is davg - At R At mass performing UCM in a circle of radius "R" and uses the period