Midterm 3 – 3/30/10
Name, sect. no.
MC1
acom= α R
a = 6 * 0.5 = 3 m/s2
Δxcom = ½ a t2
Δxcom = 13.5 m
MC2
Initially, Fx = Fy = 120 N,
so mg = 240
Now write Στ = 0 about y when
the support is moved to z: +2z
* 240 + (- 3z*Fz) = 0, so Fz =
160 N and Fy = 80 N.
4z
MC3
Ans: C
MC4
Continuity and incompressibility.
p1 = p2 + ρgh (less pressure at 2)
Now A2v2 = A1v1 (units of m3/s),
and A2 < A1, so v2 > v1 (greater speed at 2)
y
MC5
Four situations are shown in which a red
liquid and a gray liquid are in a U-tube. (a)
label the one situation where the liquids
cannot be in static equilibrium. (b) For the
other three situations, label the density of
the red liquid as greater than, less than, or
equal to the density of the gray liquid.
unphysical
Ρred < ρgray
Ρred > ρgray
ρred = ρgray
Problem 1: A student is at rest and holds a bicycle wheel with I= 1.2 kg m2. The
wheel is rotating with ω = 3.9 rev/s; as seen from overhead, the rotation is
counterclockwise. This is Sample Problem 11-7.
(a) What is the angular momentum (magnitude and direction – m&d) of the wheel?
Lw = I ω = 1.2 * 3.9 rev/s * 2π rad/rev = 29.4 kg – m2/s, direction is “up”
(b) What is the total L (m&d) for the system (student, wheel, stool)? Same as in (a)
(c)
If the student inverts the wheel, what is L of the wheel (m&d)?
29.4 kg – m2/s, direction is “down”
(d) What is the total L (m&d) for the system after the wheel is inverted?
Same as in (b) and (a): 29.4 kg – m2/s, direction is “up”
(e) If the composite rigid body (student, wheel, stool) has rotational inertia I = 6.8
kg·m2, with what angular speed and in what direction does the composite body
rotate after the inversion of the wheel?
Li =+29.4 = Lf = +6.8 * ωcomposite – 29.4.
Thus,
58.8/6.8 = ω = 8.6 rad/s = 1.4 rev/sec counterclockwise
Problem 2: Consider an orange rock that is shot up from the surface of the earth against the
force of gravity.
(a) what is the gravitational force between the earth and the rock when the rock is at an infinite
distance? F = GmM/r2, so when r →∞, F→ zero
(b) What is the gravitational potential energy when the rock is at an infinite distance?
U = zero as well (need not know the expression to know this)
(c)
What is the sign of the work done by gravity as the rock moves from the Earth’s surface to
an infinite distance? Wg = ∫Fg • dr, F and dr are in opposite directions, so W is negative
(d) Write an expression for the work done by gravity as the rock moves from R to infinity.
Wg = ∫GmM/r2dr
(e) Integrate the expression in part (d)
Wg = ∫GmM/r2dr = GmM/∞ - GmM/R = - GmM/R
(work done by gravity while moving the rock from R to ∞)
(f)
Using ΔU = -W, write an expression for the potential energy at R.
ΔU = U∞ - UR = + GmM/R → UR = - GmM/R
0