Define scalar quantities and vector quantities. How do you distinguish them? Wha

Question

Define scalar quantities and vector quantities. How do you distinguish them? What are the differences? Are they added or subtracted the same way? Explain. Show simple graphical representations of A + B and A - B (A and B are completely different vectors). Define an elastic collision, and state its important characteristics. Which energies are conserved during an elastic collision (i. e. kinetic energy, total energy, or both)? Define what an inelastic collision is, clearly stating its essential properties. Which physical quantities are conserved during an inelastic collision? Define a perfectly inelastic collision, and denote its defining characteristics. Which physical quantities are conserved during a perfectly inelastic collision? Identify whether the following quantities are scalars or vectors, and which of these are always conserved: (1) velocity; (2) speed; (3) momentum; (4) total momentum; (5) kinetic energy; (6) potential energy; and (7) total energy. Ball A, moving at 12 m/sec, collides elastically with Ball B, initially at rest, as shown in the figure at right. If both balls have the same mass, what is the final velocity of Ball A? Show all of your calculations. Two 1-kg carts with spring bumpers undergo a collision on a frictionless track as shown in the before and after pictures on the right. What is the value of the total momentum of the system before and after the collision? Explain your reasoning as to why it has these values.

Explanation / Answer

1b)

m1 = m2 = m

u1x = 12*sin60 = 6sqrt3      u2x = 0

u1y = -12*cos60 = -6         u2y = 0

after collision

V1x = 0        v1y = v1

v2x = V2      v2y = 0

along horizantal

Pix = Pfx

m1*u1x + m2*u2x = m1*v1x + m2*v2x

6*sqrt3 = v2x

along y

m1*u1y + m2*u2y = m1*v1y + m2*v2y

-6 + 0 = v1y

v1 = sqrt(v1x^2 + v1y^2)

v1 = 6 m/s <<-------answer

m1 = 1                 m2 = 1 kg

u1 = +4m/s              u2 = -4 m/s

iniital momentu Pi = m1*u1 + m2*u2 = (1*4) - (1*4) = 0

v1 = -4 m/s                   v2 = +4 m/s

final momentum Pf = (m1*v1) + (m2*v2)

Pf = -(1*4)+(1*4) = 0

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