cahier physique - physics workbook

GIVE ME A BREAK, DON'T PLAY WITH THE MATERIAL.
DISCUSSION: In class we learned that a projectile motion can be divided into 2 components: a horizontal motion and a vertical motion.
Along the horizontal, the projectile moves in a straight line at a constant speed. (acceleration is zero) and we can use the equation : x = Vix t. Vix is the x-component of the initial velocity Vi. x is the horizontal displacement of the projectile (how far it travels along the x-axis.) (Vix = Vi cos(angle) )
Along the vertical, the object is in free-fall. It accelerates toward the EArth with an acceleration of g (9.8m/s/s). The vertical component of the velocity increases by 9.8m/s every second : Vy = g t = 9.8 t.
(for the lab, the y-component of the initial velocity is zero Viy = 0). We also have, along the vertical, y = 0.5 g t²

y is the displacement along the vertical. (height from which the object is dropped.)

For this we will use the 2 equations of motion: 1) x = Vx t and 2) y = 0.5 g t²
From equation 1) solve for t = _________
Substitute the expression of t you just found into equation 2) and solve for y:
y = _____________. (use only x, g, Vx to find y).

Is it surprising ? The ball follows what kind of trajectory ? a _________
.
y = k x² is the equation of a parabola. In our case k = ____________

PURPOSE: You will predict X using the equations of motion and check your prediction. You will also use a graph to compute the flight time and then check your computation.

PROCEDURE:

STEP1: Adjust the ramp so that A is 10cm above the table. Measure the horizontal par BC. Release the ball from A and time how long the ball takes to cross over BC. Along BC the ball has a constant velocity = Vx. We neglect frictions. Find the velocity Vx of the ball using Vx = BC / t . Make at least three runs and find the average velocity. Record your data in TABLE A.

TABLE A

trial	time (t) (s)	velocity (Vx) (cm/s)
1
2
3
average Vx
vertical distance Y
calculated X

STEP2: Measure and record Y in TABLE A.
From the equation Y = 0.5 g ( X²/Vx² ). solve for X . Then use the values of Y and Vx from TABLE A to predict X. Record in TABLE A what X should be according to your calculations.

STEP3: Place a cup or a piece of paper at the calculated distance X from the edge ot the table. Roll the ball down the ramp to see if your calculated prediction was correct. Is your prediction good ? ________________

ANALYSIS/GOING FURTHER

1) was the purpose of this lab accomplish ? why ?

2) If you increase the height of the ramp to 20cm. Is Vx will increase?decrease?stay the same ?

3) There was another way to find Vx. You could have used the conservation of energy:
potential energy at A = kinetic energy at B.
m g H = 1/2 m Vx². Can you solve for Vx ? Vx = _______________.
If H = 10cm, Vx = ____________. Is it close to the value found previously ?_____________

4) A projectile is fired, from the ground, with an initial velocity Vi of 150m/s (Vi = 150m/s) at an angle of 30 degrees with the horizontal. try without hint. (specially if you aim at the advanced Physics ! )
A) Find the x-component of Vi : Vix = ________________
Find the ycomponent of Vi : Viy = ________________
B) Then fill the table. (compute the velocity at different time)

time t (s)	x-component of the velocity Vx hint: use Vx = Vix	y-component of the velocity Vy hint: use Vy =Viy - 9.8 t	magnitude of the velocity V hint: V² = Vx² + Vy²	Draw the vector V and find the direction. (angle with x-axis) hint: trace Vx, then Vy on top of Vx. (tail to head) Then trace V by connecting the tail of Vx to the head of Vy. angle = tan(Vy/Vx) . Show in which quadrant lies V.. Vx, Vy and V form a right triangle. V is the hypotenuse, Vx and Vy the legs.
0	Vx = Vix	Vy = Viy =
2 s
10s

C) Can you find how long it will take for the projectile to reach the top of the trajectory ?
(hint: Vy = 0 at the top, use Vy = Viy - 9.8 t and solve for t with Vy = 0)

T max = ______________

D) When t = 2 Tmax (twice the time for the projectile to reach the highest point), the projectile reaches the ground.
Can you find the horizontal distance covered (range) ?
( hint: use X = Vix t with t = 2 Tmax and Vix = 150 cos(30) . Tmax was calculate previously)

E) optional:
Find the equation of the trajectory of the projectile : y = ________ x²