F A C U L T Y O F E D U C A T I O N Department of Curricuum and Pedagogy Physics Dynamics: Springs Science and Mathematics Education Research Group Supported by UBC Teaching and Learning Enhancement Fund 2012-2013
Question Springs in Tite Series and Parae k s
Question Tite Vertica Springs I A 0.50 m spring with spring constant 100 N/m hangs from the ceiing. A 2.0 kg bock is tied to the spring. How much does the spring stretch? (Use g = 10 m/s 2 ) A. 2.0 m B. 0.70 m C. 0.52 m D. 0.20 m E. 0.020 m 0.5 m 0.5 m? 2 kg
Comments Soution Answer: D Justification: The 2.0 kg mass appies a 20 N force downwards on the spring (this force is caused by gravity the pu of the Earth). In order to support the 20 N downward force, the spring must appy a 20 N force upwards. Assume upwards is positive and downwards is negative. F kd S 20 N ( 100 N/m) d d 0.20 m Therefore, the spring wi stretch (etend downwards) by 0.20 m. The tota ength of the spring wi be 0.70 m, but the stretch is ony 20 cm.
Question Tite Vertica Springs II A spring with ength and spring constant k s hangs from the ceiing. A mass m is paced on the spring and increases the ength of the spring by. By how much wi a 2m mass stretch the spring from its origina - un-stretched state? A. The spring wi stretch by 2. B. The spring wi stretch by. C. The spring wi stretch by 0.5. m? m m
Comments Soution Answer: A Justification: The tension force of a spring is directy proportiona to the amount it is compressed or stretched from its rest position: F = -k. A 2m mass wi eert a downward force twice as arge as a 1m mass. Thus the spring must stretch twice as much in order to hod the 2m mass.
Question Tite Vertica Springs III A singe spring is stretched by when a mass m is attached. An identica spring is joined in series to the first spring. How much wi the two springs stretch when a mass m is attached? (Assume the springs have negigibe mass) m A. The spring wi stretch by 2 since each spring stretches by B. The spring wi stretch by since the spring constant remains the same C. The spring wi stretch by 0.5 since there are 2 springs hoding the mass D. There is not enough information to answer
Comments Soution Answer: A Justification: For springs with negigibe mass, the tension aong them has to be constant at a points. Since the tension of the spring hoding the mass is equa to mg, the tension of the other spring is aso mg. Each spring stretches by, causing a tota stretch of 2. This means that two identica springs connected in series wi stretch twice as much as one spring woud have stretched! m
Question Tite Vertica Springs IV Two identica springs (each with spring constant k s ) are connected in series as shown. What is the spring constant of the two springs together (k T )? (Assume the springs have negigibe mass) A. k T = 2k s B. k T = k s C. k T = 0.5k s D. Cannot be determined
Comments Soution Answer: C Justification: From question III, we earned that doubing the ength of a spring wi cause it to stretch twice as much. The spring becomes weaker, since a smaer force is required to stretch it by the same amount. The spring constant is therefore haved: F T F k (2 ) k T k d T F 1 F 1 2 2 2 k s
Question Tite Vertica Springs V A singe spring is stretched by when a mass m is attached. An identica spring is joined in parae to the first spring. How much wi the two springs stretch when a mass m is attached to both springs simutaneousy? (Assume the springs have negigibe mass) A. The spring wi stretch by 2 since each spring stretches by B. The spring wi stretch by since the spring constant remains the same m C. The spring wi stretch by 0.5 since there are 2 springs hoding the mass m
Comments Soution Answer: C Justification: The downward force mg is now supported by 2 separate springs. Each spring must then eert an upward force mg equa to 2. Therefore, each spring wi stretch haf as much, or. 2 2 m
Question Tite Vertica Springs VI Two identica springs (each with spring constant k s ) are connected in parae as shown. What is the spring constant of the two springs together (k T )? (Assume the springs have negigibe mass) A. k T = 2k s B. k T = k s C. k T = 0.5k s D. Cannot be determined
Comments Soution Answer: A Justification: We earned from question 5 that two springs in parae wi stretch haf as much as a singe spring with the same mass attached. It requires twice as much force to stretch the two springs. The two springs are stronger and have twice the spring constant. F k d F k T T kt( ) 2 2F F 2 2k s
Question Tite Vertica Springs VII Which coection of springs has the argest spring constant? A. B. C. D. E. A have the same spring constant
Comments Soution Answer: D Justification: Spring A has 3 springs in series, so the spring constant is k s. 3 Spring B and Spring C have springs connected in parae and in series. The springs in parae stretch 0.5, and the singe spring stretches. The tota stretch is 1.5, giving a spring constant of Spring D has 3 springs in parae, so the spring constant is 3k s. For this case: F k d F k T T kt( ) 3 3F F 3 3k s 2k s 3