1008 Stones thrown vertically upward | Rectilinear Translation

Problem 1008
A stone is thrown vertically upward from the ground with a velocity of 48.3 ft per sec (14.72 m per sec). One second later another stone is thrown vertically upward with a velocity of 96.6 ft per sec (29.44 m per sec). How far above the ground will the stones be at the same level?
 

1007 Finding when and where the stones pass each other | Rectilinear Translation

Problem 1007
A stone is dropped from a captive balloon at an elevation of 1000 ft (304.8 m). Two seconds later another stone is thrown vertically upward from the ground with a velocity of 248 ft/s (75.6 m/s). If g = 32 ft/s2 (9.75 m/s2), when and where the stones pass each other?
 

1005 Finding the depth of well by dropping a stone | Rectilinear Translation

Problem 1005
A stone is dropped down a well and 5 sec later, the sounds of the splash is heard. If the velocity of sound is 1120 ft/sec (341.376 m/s), what is the depth of the well?
 

1004 Relative velocity | Rectilinear Translation

Problem 1004
A ball is dropped from the top of a tower 80 ft (24.38 m) high at the same instant that a second ball is thrown upward from the ground with an initial velocity of 40 ft/sec (12.19 m/s). When and where do they pass, and with what relative velocity?
 

1003 Return in 10 seconds | Rectilinear Translation

Problem 1003
A stone is thrown vertically upward and return to earth in 10 sec. What was its initial velocity and how high did it go?
 

1002 Location of warning torpedo | Rectilinear Translation

Problem 1002
On a certain stretch of track, trains run at 60 mph (96.56 kph). How far back of a stopped train should be a warning torpedo be placed to signal an oncoming train? Assume that the brakes are applied at once and retard the train at the uniform rate of 2 ft/sec2 (0.61 m/s2).
 

Curvilinear Translation (Projectile Motion)

Projectile motion follows a parabolic trajectory. The vertical component of projectile is under constant gravitational acceleration and the horizontal component is at constant velocity. For easy handling, resolve the motion into x and y components and use the formulas in rectilinear translation.
 

Form the figure below:

$v_{ox} = v_o \, \cos \theta$

$v_{oy} = v_o \, \sin \theta$

 

000-projectile-general.gif

 

Kinematics

Motion of a Particle
Particle is a term used to denote an object of point size. A system of particles which formed into appreciable size is termed as body. These terms may apply equally to the same object. The earth for example may be assumed as a particle in comparison with its orbit, whereas to an observer on the earth, it is a body with appreciable size. In general, a particle is an object whose size is so small in comparison to the size of its path.
 

Rectilinear Translation (Motion Along a Straight Line)

Dynamics

Dynamics is the branch of mechanics which deals with the study of bodies in motion.
 

Branches of Dynamics
Dynamics is divided into two branches called kinematics and kinetics.

Kinematics is the geometry in motion. This term is used to define the motion of a particle or body without consideration of the forces causing the motion.

Kinetics is the branch of mechanics that relates the force acting on a body to its mass and acceleration.
 

Symbols and Notations
s = distance

820 Unsymmetrical I-section | Moment of Inertia

Problem 820
Determine the moment of inertia of the area shown in Fig. P-819 with respect to its centroidal axes.
 

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