646 



SCIENCE 



[N. S. Vol. XLI. No. 1051 



Before we can determine the effect of a con- 

 stant unbalanced force in changing the motion 

 of a body, we must study some simple types of 

 motion. 



6. Some Simple Types of Motion. — (1) Uni- 

 form motion in a straight line with constant 

 speed. Define velocity. d = st. 



(2) Constantly changing speed, linear mo- 

 tion. Define acceleration of speed. Derive 

 formulas : s^at; d = iat^ ; etc. ; and 

 s = s„ ■+ ai ; d^s„t -\- iat^ ; etc. 



(3) Parabolic motion, combination of (1) 

 and (2) at right angles. Formulas. 



(4) Uniform circular motion. Constant 

 speed but constantly changing velocity. De- 

 rive a^s'^/r. Distinguish tangential from 

 centripetal acceleration. 



7. Type of Motion Due to a Constant Gravi- 

 tational Force. — (1) Atwood's machine, 

 balanced forces; speed constant. 



(2) Atwood's machine, small unbalanced 

 force ; d , — f^; positive acceleration. 



(3) Atwood's machine, small retarding force ; 

 negative acceleration. 



(4) Ball rolling down an inclined plane, or 

 Fletcher's apparatus ; s ^—'t, d.—'t'^; accelera- 

 tion constant. 



(5) Water jet against blackboard, parabolic 

 path; dr^f^. 



(6) Ball rolling off table ; measure 5^. Same 

 for all bodies. 



Conclusion: The motion produced is one 

 with constant acceleration. 



8. Variation of Acceleration with the Force 

 Acting on a Given Body. — (1) Atwood's ma- 

 chine, various small unbalanced forces. 



(2) Frictionless carriage on smooth hori- 

 zontal plane. 



Conclusion: The acceleration is directly 

 proportional to the force. 



9. Measurement of Force Required to Give 

 Centripetal Acceleration to a Given Body. — 

 (1) Swing 50 or 100 gm. on the end of a rubber 

 band or spiral spring and determine the stretch 

 during rotation at a fixed rate. Measure the 

 gravitational force required to produce the 

 same stretch. Compute the centripetal accel- 

 eration and show that the force required to 



produce it is to the weight of the body as the 

 centripetal acceleration is to the acceleration 

 of gravity. 



(2) The centripetal force in the case of a 

 mass rotating in a horizontal plane and free 

 to slide along a rod may be measured directly 

 by the weight required to produce the accelera- 

 tion. Make the same computation as in (1). 



Conclusion: The unbalanced force required 

 to produce centripetal acceleration is equal to 

 that required to give the same body an equal 

 linear acceleration. Combining this with the 

 conclusion of §8 we see that the acceleration 

 produced by an unbalanced force acting on 

 any given body is proportional to the force 

 and is in the direction of the force, whether 

 it is tangential or centripetal. 



10. Nongravitational Forces, Magnetic, Elec- 

 tric, Frictional, etc. — Can be balanced by grav- 

 itational forces; produce the same effect when 

 unbalanced; can be measured in terms of the 

 gravitational force which will balance them or 

 which will give the same acceleration to the 

 same body. From our experience with gravi- 

 tational forces we generalize and assume that 

 whenever a body is being accelerated it is being 

 acted upon by an unbalanced force ; and if the 

 known forces acting on the body are insuffi- 

 cient to account for its acceleration, we imme- 

 diately postulate the existence of another force 

 and experiment to find out what physical prop- 

 erties of the body in question and of the other 

 bodies concerned, determine the amount of the 

 force. 



We have studied the relative effect of vari- 

 ous forces upon the same tody and arrived at 

 the important generalization that whether the 

 acceleration produced be tangential or cen- 

 tripetal, it is proportional to the force and in 

 the direction of the force. We will not study 

 the effect of the same force on various bodies. 



B. Inertia or Mass 



11. Introduction. — The fact that force is 

 necessary to change the velocity of any body 

 implies a tendency to persist in uniform mo- 

 tion and to resist a change of motion. This 

 property of bodies is called inertia. The easier 

 it is to accelerate a body, the less its inertia, of 



