Chapter13 Kinetics of a Particle: Force and Acceleration Sec. 13.1 ~ 13.6 . Homework Prob. 15, 25, 58, 79, 101, 107
13.1 Newton’s Laws of Motion
1st Law: If a particle, originally at rest or moving with a constant velocity, is not subjected to an
unbalanced force, then it will remain in this state.
3rd Law: The mutual forces of action and reaction between two particles are equal, opposite, and
13.4 Motion in Rectangular Coordinates
FmaFmaFma？？？; ; ；；；xxyyzz
Procedure for analysis
• Select the inertial coordinate system.
Draw the free-body diagram. •
• Identify the acceleration to show the kinetic diagram.
• List the equations of motion.
• Solve the kinematics problem.
Important Points for Solving Problem
Equations of motion
• Friction: Ff = ？k N. Ff always opposes the motion of the particle relative to the
• Spring: Fs = k (l – l0).
• a = a(t); v(t) = ?a(t)dt s(t) = ?v(t)dt
• a = a(s); ?a(s)ds = ?v(s)dv
• Make sure the positive inertial coordinate directions used for writing the kinematic
equations are the same as those used for writing the equations of motion. Example 3:
The 2-lb collar C fits loosely on the smooth shaft. If the spring is unstretched when s
= 0 and the collar is given a velocity of 15 ft/s, determine the velocity of the collar
when s = 1 ft. (Prob. 13-38)
13.5 Motion in N-T Coordinates
FmaFmaF？？？; ; 0 ；；；ttnnb
3 22~?dy，? 1;?，：(2dx ；)dvv?，??，aa？？？ and tn2 dt，dy
The package has a weight of 5 lb and slides down the chute. When it reaches the
curved portion AB, it is traveling at 8 ft/s (！ = 0o). If the chute is smooth, determine the speed of the package when it reaches the intermediate point C (！ = 30o) and when
it reaches the horizontal plane (！ = 45o). Also, find the normal force on the package at C. (Prob. 13-70)
Example Prob. 13-77;p133；
13.6 Motion in Cylindrical Coordinates
2 ！！！FmrrFmrrFmz？；？;？(); (2); ；；；rz！
A positive ( means that it’s measured in the positive direction of ！.
Rod OA rotates counterclockwise with a constant angular velocity of 5 rad/s. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other slides over the horizontal curved rod, of which the shape is described by the equation r = 1.5(2 - cos！) ft. If both collars weight 0.75 lb, determine
the normal force which the curved rod exerts on one collar at the instant = 120o. Neglect friction. (Prob. 13-89)
Using air pressure, the 0.5-kg ball is forced to move through the tube lying in the horizontal plane and having the shape of a logarithmic spiral. If the tangential force exerted on the ball due to the air is 6 N, determine the rate of increase in the ball’s speed at the instant ！ = ，/2. What direction does it act in? (Prob. 13-106)
13.3 Equation of Motion for a System of Particles
The Equation of motion will be extended to a System of Particles. For ith particle:
FandfiiHere represent the resultant external force and internal force respectively.
All these equations are added together vectorially, we obtain: ；？；;；maFf ；？；maF iiiiiii
and no mass is leaving the system, we have: And consider the relation ；？mrmriiG
and maF？； ；？mamaGiiG