Question

1. Which weights more, a box filled with 300grams of marbles or a box filled with 300grams of feathers. Assume both boxes have equal mass. (a) There is not enough data to answer the question (b) They weigh the same (c) a box filled with 300gram of marbles (d) a boxed filled with 300grams of feathers.

*is this a trick question? or I'm possible over-thinking it?? I would think the OBVIOUS answer is B.

2. In our uniformly accelerated motion lab, we applied a quadratic polynomial, y=Ax²+Bx+C, to the data of the position vs time graph. Given x=x₀+v₀t+1/2at², what do the coefficients correspond to? (a) C=initial position, B=initial velocity*t, A=initial acceleration*t² (b) C=initial position, B=initial velocity, A=initial acceleration*(1/2) (c) C=initial position, B=initial velocity*t, A=(1/2)*acceleration*t² (d) C=initial position, B=initial velocity, A=accleration*(1/2)

3. For the object experiencing circular motion, if the radius is doubled: (a) the acceleration is unchanged (b) the accerleration is doubled (c) the acceleration is halved (d) the acceleration is quadrupled

Answer 1

1)
Since they have same masses, they weigh the same.

2)
y = Ax² + Bx + C
At x = 0,
y = C, which is the coefficient of initial distance.
Velocity, dy/dt = (dy/dx) (dx/dt)
= (2Ax + B)(vo + at)
At time t = 0,
velocity = 2Axvo + Bvo
At x = 0, B is the coefficient of initial velocity vo.

Acceleration, d²y/dt² = (d²y/dx²) (d²x/dt²)
= (2A)(a)
So, A = 1/2 initial acceleration.

c)
Centripetal force, F = mv²/R
Acceleration, a = F/m = v²/R
So, if the radius is doubled, acceleration will be halved.