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ENGINEERING MECHANICS 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) Motion with constant velocity (uniform motion)

Motion with constant acceleration

Free-falling body

Note: From motion with constant acceleration, set vi = 0, vf = v, s = h, and a = g to get the free-fall formulas. Motion with variable acceleration

Where: = distance = height = velocity = initial velocity = final velocity = acceleration = acceleration due to gravity (g = 9.81 m/s2 in SI = 32.2 ft/s2 in English) = time Note: • is positive (+) if • is negative (-) if

is increasing (accelerate). is decreasing (decelerate).

• •

is positive (+) if the particle is moving downward. is negative (-)if the particle is moving upward.

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?

For tstone (free-falling body):

For tsound (uniform motion):

Thus,

English System

For h = 88 759.73 ft

(not okay!)

For h = 353.31 ft

(okay!) Thus, h = 353.31 ft

→ answer

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? Solution in English System

For the first stone:

For the second stone

answer Problem 1009 A ball is shot vertically into the air at a velocity of 193.2 ft per sec (58.9 m per sec). After 4 sec, another ball is shot vertically into the air. What initial velocity must the second ball have in order to meet the first ball 386.4 ft (117.8 m) from the ground?

Solution in English System

Thus,

First ball:

Use Second ball:

answer Problem 1010 A stone is thrown vertically up from the ground with a velocity of 300 ft per sec (91.44 m/s). How long must one wait before dropping a second stone from the top of a 600-ft (182.88-m) tower if the two stones are to pass each other 200 ft (60.96 m) from the top of the tower? English System Solution

Stone from the ground:

Stone from the top of the tower:

Let t2 = time to wait before dropping the second stone

With t = 17.19 sec

With t = 1.44 sec (meaningless) Use

answer

Problem 1011 A ship being launched slides down the ways with constant acceleration. She takes 8 sec to slide (the first foot | 0.3048 meter). How long will she take to slide down the ways if their length is (625 ft | 190.5 m)? Solution

where Thus

English Units

answer

SI Units

answer

Problem 1012 A train moving with constant acceleration travels 24 ft (7.32 m) during the 10th sec of its motion and 18 ft (5.49 m) during the 12th sec of its motion. Find its initial velocity and its constant acceleration. Solution in English Units

→ equation (1) → equation (2) Equation (1) minus equation (2) answer From equation (1) answer Problem 1019 The motion of a particle is given by the equation seconds. Compute the values of and when Solution 1019

HideClick here to show or hide the solution

When t = 2 sec

where .

is in meter and

in

answer

answer

View more...
Motion with constant acceleration

Free-falling body

Note: From motion with constant acceleration, set vi = 0, vf = v, s = h, and a = g to get the free-fall formulas. Motion with variable acceleration

Where: = distance = height = velocity = initial velocity = final velocity = acceleration = acceleration due to gravity (g = 9.81 m/s2 in SI = 32.2 ft/s2 in English) = time Note: • is positive (+) if • is negative (-) if

is increasing (accelerate). is decreasing (decelerate).

• •

is positive (+) if the particle is moving downward. is negative (-)if the particle is moving upward.

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?

For tstone (free-falling body):

For tsound (uniform motion):

Thus,

English System

For h = 88 759.73 ft

(not okay!)

For h = 353.31 ft

(okay!) Thus, h = 353.31 ft

→ answer

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? Solution in English System

For the first stone:

For the second stone

answer Problem 1009 A ball is shot vertically into the air at a velocity of 193.2 ft per sec (58.9 m per sec). After 4 sec, another ball is shot vertically into the air. What initial velocity must the second ball have in order to meet the first ball 386.4 ft (117.8 m) from the ground?

Solution in English System

Thus,

First ball:

Use Second ball:

answer Problem 1010 A stone is thrown vertically up from the ground with a velocity of 300 ft per sec (91.44 m/s). How long must one wait before dropping a second stone from the top of a 600-ft (182.88-m) tower if the two stones are to pass each other 200 ft (60.96 m) from the top of the tower? English System Solution

Stone from the ground:

Stone from the top of the tower:

Let t2 = time to wait before dropping the second stone

With t = 17.19 sec

With t = 1.44 sec (meaningless) Use

answer

Problem 1011 A ship being launched slides down the ways with constant acceleration. She takes 8 sec to slide (the first foot | 0.3048 meter). How long will she take to slide down the ways if their length is (625 ft | 190.5 m)? Solution

where Thus

English Units

answer

SI Units

answer

Problem 1012 A train moving with constant acceleration travels 24 ft (7.32 m) during the 10th sec of its motion and 18 ft (5.49 m) during the 12th sec of its motion. Find its initial velocity and its constant acceleration. Solution in English Units

→ equation (1) → equation (2) Equation (1) minus equation (2) answer From equation (1) answer Problem 1019 The motion of a particle is given by the equation seconds. Compute the values of and when Solution 1019

HideClick here to show or hide the solution

When t = 2 sec

where .

is in meter and

in

answer

answer

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