PHY 2053 Discussion
Review: Chapter 3
1. Vectors
1) Two properties and two operations of vectors:
Properties: Magnitude & direction
Operation: Addition & scalar multiplication
2) How do you express a vector graphically, its magnitude and direction?
We use an arrow with its length proportional to the magnitude; The orientation of the arrow represents the direction of the vector.
3) How do you express a vector A algebraically, its magnitude and direction?
We use components Ax (=Acosθ) and Ay. (=Asinθ).
Magnitude: A = √(Ax²+Ay²), Direction: θ = tan⁻¹(Ay/Ax)
4) Graphical method to express A±B:
A+B: Place the tail of B at the head of A; A+B is the arrow drawn from the tail of A to the head of B
A-B: Place both tails together; A-B is the arrow drawn from the head of B to the head of A.
5) Algebraic method to calculate A±B:
Add or subtract each component: A±B = (Ax±Bx, Ay±By)
6) What is the negative of a vector A?
The vector that has the same magnitude as A but opposite direction.
7) We need to calculate the magnitude and direction of A+B. What do we do?
Express A & B in component forms, add the two vectors algebraically and then convert it to magnitude and direction.
8) I expect the resultant vector lies in the 3rd quadrant, but I got the resultant angle in the 1st quadrant. What should I do?
Add 180˚ to your result. Estimate the result graphically before algebraic calculation.
2. Projectile motion
1) Is the horizontal motion and vertical motion dependent or independent?
Independent. So you should not mix them up.
2) They have one quantity in common:
Time.
3) The acceleration in the horizontal direction and that in the vertical direction:
Horizontal: ax = 0, Vertical: ay = -g = -9.8 m/s2 (Upward positive)
4) Expression of x- and y-component of the initial velocity in terms of the magnitude and projection angle:
v0x = v0cosθ, vy = v0sinθ
5) What are the x- and y-component of velocity at the peak of the projectile motion?
vx = v0x, vy = 0
6) A ball is thrown from a top of a building, whose height is known. How do we get horizontal range of the ball?
Using the y-displacement equation, we calculate the time when the ball hits the ground. Then plug the time in the x-displacement equation.
7) A ball is thrown toward a wall from a known distance. How do we get the height of the ball when it hits the wall?
We use the x-displacement equation and get the time when the ball hits the wall. Then calculate the y-displacement at that time.
3. Relative Velocity
1) Definition of vAB:
Velocity of the object A relative to the object B
2) A person walks on a train at vPT and the train moves at vTE relative to the earth. What is the velocity of the person relative to the earth vPE?
vPE = vPT + vTE
3) A boat moves at a constant speed relative to water. Does it move faster when it goes downstream or upstream?
Downstream
4) Describe the general strategy to solve relative velocity problems in 2D.
Express known quantities in components. Then set up equations for each component.
5) A boat crosses the river flowing due east at vRE. The boat heads due north relative to the water at vBR. Find the speed of the boat relative to the shore vBE.
vBE = √(vBR2+vRE2)