Projectile Motion
Projectile Motion
The purpose of this lab is to study the properties of projectile motion. From the motion of a steel ball projected horizontally, the initial velocity of the ball can be determined from the measured range. For a given initial velocity, the projectile range will be measured for various initial angles, and also calculated by applying the theory for motion with constant acceleration. For further background information, refer to the sections in your textbook on projectile motion and motion with constant acceleration.
THEORY For a given initial velocity, v0 , and initial position, s0 ,the position of a particle, s, as a function of time, undergoing constant acceleration, a is given by sr = sr 0 + vr 0 t + 12 ar t 2 ( 1 )
This is a vector equation and can be broken up into its x, y, and z components. Since the motion is in a plane, we need only look at the x and y components. If we neglect air resistance, the acceleration in the y direction is -g, due to gravity. The acceleration in the x direction is zero. Hence, the vector equation (1) becomes two scalar equations:
If we eliminate t in Eqs.(5) we get y as a function of x. gx2 and solving for vo we get x = x0 + v 0x t (2) y=y+v t-1gt2
0 0y In terms of the angle θ, and the initial speed vo, the initial velocity components are v0x=v0cosθand v0y=v0sinθ A. For the case in which θ = 0° (initial velocity is horizontal), Eqs. (2) and (3) become x=vtand y=h-1gt2 0
2 (3)
(4) 2 (5) y = h − 2v2 (6) o
When the object hits the floor the x and y positions are x = R and y = 0. Hence, Eq. (6) becomes
0 = h − gR 2
1
Projectile Motion
2v2 o
❏ Spring gun set-up ❏ Gun mounted on frame w/ protractor ❏ Hook collar w/ pointer ❏ 2 Bench clamps ❏ 2 Aluminum bar supports w/ wing nut ❏ Short rod
❏ Spring gun ball ❏ Bar level ❏ Two-meterstick ❏ Plumb-bob
❏ Masking tape ❏ Paper v 0 = R g for the case θ = 0° 2h
(7) B. Now consider the case in which θ ≠ 0° (initial velocity is not horizontal). If we solve Eq.
The purpose of this lab is to study the properties of projectile motion. From the motion of a steel ball projected horizontally, the initial velocity of the ball can be determined from the measured range. For a given initial velocity, the projectile range will be measured for various initial angles, and also calculated by applying the theory for motion with constant acceleration. For further background information, refer to the sections in your textbook on projectile motion and motion with constant acceleration.
THEORY For a given initial velocity, v0 , and initial position, s0 ,the position of a particle, s, as a function of time, undergoing constant acceleration, a is given by sr = sr 0 + vr 0 t + 12 ar t 2 ( 1 )
This is a vector equation and can be broken up into its x, y, and z components. Since the motion is in a plane, we need only look at the x and y components. If we neglect air resistance, the acceleration in the y direction is -g, due to gravity. The acceleration in the x direction is zero. Hence, the vector equation (1) becomes two scalar equations:
If we eliminate t in Eqs.(5) we get y as a function of x. gx2 and solving for vo we get x = x0 + v 0x t (2) y=y+v t-1gt2
0 0y In terms of the angle θ, and the initial speed vo, the initial velocity components are v0x=v0cosθand v0y=v0sinθ A. For the case in which θ = 0° (initial velocity is horizontal), Eqs. (2) and (3) become x=vtand y=h-1gt2 0
2 (3)
(4) 2 (5) y = h − 2v2 (6) o
When the object hits the floor the x and y positions are x = R and y = 0. Hence, Eq. (6) becomes
0 = h − gR 2
1
Projectile Motion
2v2 o
❏ Spring gun set-up ❏ Gun mounted on frame w/ protractor ❏ Hook collar w/ pointer ❏ 2 Bench clamps ❏ 2 Aluminum bar supports w/ wing nut ❏ Short rod
❏ Spring gun ball ❏ Bar level ❏ Two-meterstick ❏ Plumb-bob
❏ Masking tape ❏ Paper v 0 = R g for the case θ = 0° 2h
(7) B. Now consider the case in which θ ≠ 0° (initial velocity is not horizontal). If we solve Eq.