Mechanics Lab (Civil Engineers) Nae (please print): Tutor (please print): Lab group: Date of lab: Experients In the session you will be divided into groups and perfor four separate experients: (1) air-track collisions; () static and kinetic friction; (3) flywheel experient; (4) ass-spring oscillations. Write-Up and Subission Experiental data should be recorded and analysed during the laboratory session. Results and analysis should only be subitted on this worksheet. Subission is at the end of the lab and it is your responsibility to ensure that your worksheet is handed in. Work will be returned when everybody s report has been arked. This report constitutes 10% of the total arks for the Mechanics unit. Mechanics (Civil) Labs - 1 David Apsley
1. Air Track Collisions The air track provides a nearly frictionless environent for experients on objects oving in a straight line. You will use two gliders, one initially stationary near the iddle of the track and one set in otion by an elastic syste. There is also a easuring syste, which uses optical gates to deterine the speed of the gliders. optical gates electroagnet oving glider (1) stationary glider () Method The optical gates should be either side of the starting point of the stationary glider. The other glider is held against an elastic end stop by an electroagnet. When the agnet is switched off, its glider is propelled forward by the elastic. Its initial velocity can be deterined as it passes the optical gate. After the collision, the final velocities of the two gliders can be deterined as they pass one or other of the optical gates. You ay need to adjust the position of the gates so that only one glider is passing a gate at a tie, and you ay need to catch one of the gliders. The ass of each glider is roughly 00 g, but you should easure these accurately. There are soe additional asses that can be added to one or both of the gliders. Do the experient with three cobinations of asses. Write 1 and for the asses of the two gliders, u 1 and u for the initial velocity of each glider, and v 1 and v for the signed velocities (negative if in the opposite direction to the initial otion). Mass of oving glider (1) Mass of stationary glider () kg kg Mechanics (Civil) Labs - David Apsley
Results Tables Record your easureents in the following table. 1 (kg) (kg) u 1 ( s 1 ) u ( s 1 ) v 1 ( s 1 ) v ( s 1 ) 0 0 0 Analyse your results in the following table. Initial oentu Final oentu Speed of (kg s 1 ) (kg s 1 ) approach ( s 1 ) Speed of separation ( s 1 ) Coefficient of restitution, e Questions 1. For each experient, calculate the total oentu before ( 1 u 1 + u ) and the total oentu after ( 1 v 1 + v ). What result do you anticipate obtaining?. For each experient, calculate speed of approach, speed of separation and thus the coefficient of restitution, inserting values in the table. speed of separation v v1 e speed of approach u1 u What would a value e = 1 ean? What would a value e = 0 ean? Suggest sources of error in the experient. Mechanics (Civil) Labs - 3 David Apsley
. Static and Kinetic Friction A ass is initially resting on an inclined slope of angle θ. As the angle is increased the coponent of weight directed down the slope increases and eventually exceeds the static friction between the ass and the slope. This can be used to deterine the coefficient of static friction (μ s ) fro μ s tan θ s where θ s is the angle of incipient otion. If the ass is given an initial push to get it oving, it will be subject to kinetic friction. Friction and downslope weight coponent will be in equilibriu (and hence the ass will just keep oving) when μ tan k θ k For 3 different objects: easure the angle θ s at which the stationary ass just starts to slide, and hence deduce the coefficient of static friction, μ s ; easure the angle θ k at which a oving ass just stops sliding, and hence deduce the coefficient of kinetic friction, μ k ; calculate the ratio μ k /μ s. Repeat this for one of the objects with an additional ass on top to increase the noral reaction. Mechanics (Civil) Labs - 4 David Apsley
Object Angle of incipient sliding, θ s Angle of incipient stopping, θ k Coefficient of static friction, μ s Coefficient of kinetic friction, μ k Ratio μ k / μ s 1 3 Object + ass By considering the balance of forces, prove analytically the result static and kinetic friction). μ tan θ (applying to both Do you expect the ratio μ k /μ s to be the sae for all aterials? On what ight it depend? Mechanics (Civil) Labs - 5 David Apsley
3. Flywheel Experient The oent of inertia I plays a siilar role in rotational echanics to that which ass does in linear echanics. r I In this experient a falling weight is used to turn a flywheel. The tie and distance of fall are easured. These ay be used to calculate the acceleration of the falling body and thence the oent of inertia of the flywheel. a Method g A weight g is attached to a string which is initially wrapped around the shaft of a flywheel. The shaft has radius r = 0.011 (diaeter ). The ass is allowed to fall a distance h and the tie taken, t, easured with a stopwatch. A constant-acceleration forula relates the fall distance to the acceleration a: 1 h at In an ideal syste, the linear acceleration, a, of the ass is related to the oent of inertia of the flywheel, I, and the acceleration due to gravity, g (=9.81 s ), by g a I 1 r (You will be able to derive this once we have covered rotational dynaics.). This can be rearranged for the oent of inertia: g I r ( 1) a Find the final velocity v of the ass fro a constant-acceleration forula and the final angular velocity ω of the flywheel by rearranging v rω Check your calculations by coparing the loss of potential energy (gh) with the gain in kinetic energy of the falling ass ( 1 v ) plus flywheel ( 1 I ω ). Repeat for a different falling weight. Mechanics (Civil) Labs - 6 David Apsley
Results Record your easureents in the following table. g (N) h () t (s) Analyse your results in the following table. Acceleration a ( s ) Moent of inertia I (kg ) Final velocity v ( s 1 ) Angular velocity ω (rad s 1 ) Loss of PE gh (J) KE of ass 1 v (J) KE of flywheel 1 I ω (J) Coent on the energy changes in the experients which types are involved; which increase and which decrease; the relative sizes of the kinetic energy of the ass and the flywheel. Suggest sources of error in the experient and ways of eliinating the. Mechanics (Civil) Labs - 7 David Apsley
Force (N) 4. Oscillations A ass is hung fro one or two equivalent springs in each of the configurations shown. The period of oscillation T is copared with that predicted theoretically: T π k eff where k eff is the equivalent effective stiffness (the stiffness of a single spring that would have the sae effect on a suspended load as a ulti-spring configuration). single spring parallel springs series springs equivalent k k k k k = F / x eff k F x Method By easuring the tension in a spring for different extensions, easure the stiffness k of a single spring. Force F and extension x are related by F = kx, and can be found as the gradient of a force vs length graph (avoiding the need to find the unstretched length of the spring and testing the linear relationship, Hooke s Law). For each ass-spring configuration shown, easure the period of oscillation by tiing a sall nuber of oscillations. Try at least two asses for each cobination. Copare easured periods with those predicted fro ass and stiffness k eff. Single spring stiffness. Length (arbitrary datu) () Force (N) 4 3 Stiffness ( = gradient of line) Run () Rise (N) Gradient (N 1 ) 1 0.0 0.04 0.06 0.08 0.10 displaced length () Mechanics (Civil) Labs - 8 David Apsley
Configuration: Mass (kg) Measured period T (s) Effective stiffness k eff (N 1 ) Predicted period T pred (s) Single spring Parallel springs Series springs Show how you deduce equivalent effective stiffnesses k eff for: parallel springs: series springs: Coplete the table for easured and predicted oscillation periods. Explain physically which cobination of ass and effective stiffness (i.e. cobination of springs) you would expect to have the shortest, and which the longest, oscillation period and why. Mechanics (Civil) Labs - 9 David Apsley