Physics Dynamics: Springs

Size: px

Start display at page:

Download "Physics Dynamics: Springs"

Annabel Brown
6 years ago
Views:

1 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

2 Question Springs in Tite Series and Parae k s

3 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 m C m D m E m 0.5 m 0.5 m? 2 kg

4 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.

5 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

6 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.

7 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

8 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

9 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

10 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 k s

11 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

12 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

13 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

14 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

15 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

16 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

Mechanics 3. Elastic strings and springs

Mechanics 3. Elastic strings and springs Chapter assessment Mechanics 3 Eastic strings and springs. Two identica ight springs have natura ength m and stiffness 4 Nm -. One is suspended verticay with its upper end fixed to a ceiing and a partice