Projectile Motion

PROJECTILE MOTION (example lab Report) •

A good projectile motion can often be obtained with the assumption that air resistance is absent.

•

In the absent of the air resistance the moving object does not slow down in the horizontal (x) direction.

•

x component of the acceleration is ax =0

•

The velocity of x component remains the same as its initial value.

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In the vertical (y) direction the projectile experiences the effect of gravity.

•

The acceleration due to the gravity.

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Projectile motion means that ax= 0 and ay equal to the acceleration due to gravity (9.80 m/s). The range is the horizontal distance traveled between launching and landing, assuming the projectile returns to the same vertical level at which it launch.

Total Mechanical Energy •

Total mechanical energy is the sum of the kinetic energy and potential energy, and it obeys the principle of conservation of mechanical energy.

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This principle in situations where there is only translation motion, as when a sled slides down a frictionless hill.

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Total mechanical energy, Ef at the bottom (hf = 0) is the same as the total mechanical energy E0 at the top. (h = h0, v0 = 0,ω0 = 0 )

½mvf2 + Iωf 2 + mghf = ½mv02 + ½Iω02 + mgh0 ½mvf2 + ½Iωf2 = mgh0

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Since each cylinder rolls without slipping the final rotational speed, ωf and the final translational speed, vf of its center of mass (ωf = v f /r ) where r is the radius of the cylinder.

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So, ½mvf2 + ½Iωf2 = mgh0 ½mvf2 + ½I(vf/r)2 = mgh0 ½vf2 (m + I/r2) = mgh0 vf2 =

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Hollow cylinder m = mh , r = rh and I = mrh2

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Solid cylinder m = mc , r =rc and I = ½ mrc2

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Solid sphere m = ms , r =rs and I = ⅖ mrs2

The translation speed at the bottom of the incline. From the equation, Hollow cylinder

Vf =

o

Vf =

=

Solid Cylinder

=

o

Vf =

o

Vf =

=

= =

o

Solid sphere

Vf =

o

Vf =

=

= =

o

The solid cylinder having the greatest translational speed and arrives at the bottom first.

Principle of Conservation of Energy Aim

: To determine the velocity of the moving object and how far it can reach to the ground.

Apparatus

: Stop watch, curve rail, marble, cylinder and circle object.

Materials

: Plasticine, box

Procedure

:

1. Set up the below apparatus. 2. The lower end of the track must be horizontal.

Object Curve Rail

Table

Plasticine Box

3. Release the marble (solid sphere) from the top of the rail and set the time as the marble reach at the end of the rail until it touch the plasticine on the floor. Repeat this step 3 times. 4. Repeat this step with another material with the thin- walled hollow cylinder and the solid cylinder and set the time exactly the same as the above step. 5. Measure the R from the table to the landing surface.

Theory Projectile Motion From the law of conservation of energy, the potential energy of a body of mass, m equals its kinetic energy that is ;

mgh = ½ mvx2 (1.1)

Where

m= the mass of the body g = the acceleration due to the gravity h = the height of the body vx= the velocity of the body

A body which is moving in a projectile motion with velocity of vx will have a range of: R = vx t

(1.2)

vx= the velocity of the body t = time taken

Result

Time (s),+ 0.01 Object

Range ,R (cm), + 0.1

1

2

3

Average

1

2

3

Average

Solid cylinder

0.19

0.22

0.23

0.21

86.9

85.9

82.7

86.5

Thin walled hollow cylinder

0.24

0.20

0.20

0.21

59.4

60.6

58.9

59.6

Solid sphere

0.17

0.18

0.20

0.18

87.4

89.9

87.4

88.2

From the experiment, the speed at a curve rail:

V solid cylinder

= R/t = 86.5 / 0.21 = 411.9 cm/s

V hollow cylinder

= R/t = 59.6 / 0.21 = 283.8 cm/s

V solid sphere

= R/t = 88.2 / 0.18 = 490.0 cm/s

From the experiment, the height of a table is 0.842 m. The translation speed at the bottom of the incline: Hollow cylinder

Vf =

o

Vf =

= = = 2.87 m/s

Solid Cylinder

Vf = Vf =

=

o

= = =3.30 m/s

Solid sphere

Vf =

o

Vf =

=

= = = 4.05 m/s

Conclusion : 1. The solid sphere has a greater speed then solid cylinder and hollow cylinder. 2. From the experiment, the value of speed at curve rail is not same then the value of translation speed at the bottom of the incline. It is because the different object influences the value of friction.