1. A 30kg child is swinging on a swing whose seat is a distance of 5.0m from the pivot point. Estimate the optimal time between “pumps” that the child should execute to increase her swinging amplitude. How does this time change for a 15.0 kg child?

• (9 got this right, 3 made a slight error, 32 didn’t answer and 10 didn’t know what to do).

• I know that the problem probably involves T = 2 (pi) (L/g)^(1/2), but I don't know how to proceed (for someone who did not know what to, this is VERY GOOD!)

• Since this is just an estimation, I used the equation T = 2 x pi (L/g)^1/2 where the mass is all concentrated at the end of the pendulum. So with L=5.0m, the optimal time is 4.5 seconds. Since the mass is not in this equation, the weight of the child doesn't matter. (This is the period; depending on how you pump this is the answer, or half this time, or some multiple of this time).

Resonance and damping

Physical Pendulum

I = mghsin() but if <<1 then: = (mgh/I)

Be careful to distinguish the physical angle from the phase angle here!

Chapter 15 problems

Rotational Inertia for Selected objects and rotation axes: HR&W Table 10-2

Review for Exam III• Rotational dynamics and kinematics:

t+ot+½ t2 2=o2 + 2(o)

I = miri2 = r x F = I

Be careful in relating linear to rotational motion. Right-hand rules for cross products and rotations.

Ang. momentum: l = rxp L=IdL/dt= In the absence of external torques Angular Momentum is

conserved! Statics: analysing/identifying torques and forces

Be careful about signs, chose your pivot points wisely Gravity F=G(m1m2/r12

2) Ug =-G(m1m2/r12) Kepler’s laws: Constant areas, T2= 42/GM a3

Fluid Statics: P=Po+gh Archemdes’ and Pascal’s principles

Fluid Dynamics: A1v1 = A2v2 P +gy + ½ v2 = const.

Review for Exam III (cont.)• Oscillations:

Mass on a spring:a= d2x/dt2 = -(k/m)[x(t) –xo]=>

x(t)-xo = A cos(tk/m

Pendula:

g/l mgl/I T = 2

Exam is 4 MC questions followed by 3 problems (3 parts each). Total 78 Points.

Review for Exam III Requests from the class

• Problem from assignments: see solutions on ONCOURSE

• Chapter 12 seemed to have the most requests, with torques, fluids and oscillations being the next most popular

Chapter 12 Problem

(c) What is the direction of the torque induced by the girl’s feet on the beam about the first support?

Chapter 14 problems

Ask yourself, what would cause the water to make it into the basement?

Chapter 14 problems

•Pressures must be equal, but areas are not. The force from the spring is 1.50kN (=20kN/m*0.05 m), so the weight of the sand must be 83.3 N (=1.5kN/18.0) so the mass of sand is 8.5kg.

Chapter 13 problems

• Y(x,t) = A sin( kx - ω t + φ)Assuming that x, y and t are all given in SI units, what are the appropriate units for A, k, ω, and φ? If these quantities are all positive, in what direction is the above wave traveling? [Units presented only isolated issues, Direction: Right/positive: 10; left/negative: 3; up/down: 2

Traveling waves

Chapter 16 Problems