19 Sep 07
Originally posted by PBE6Perfect and well said, 100% correct.
(A) The tension on the suspending cord does no work on the weight, because the force it exerts is always tangential to the movement of the weight.
(B) The air resistance always does negative work on the weight, because air resistance opposes the motion of the pendulum and therefore always acts opposite to the direction of movement of the pendulum.
(C) The ...[text shortened]... ding on whether the pendulum is on an upswing (negative work) or on a downswing (positive work).
Next question to follow.
19 Sep 07
1 edit
Originally posted by RamnedThe rain will add mass to the box without adding horizontal momentum, so the box will slow down.
Momentum
[b]6. An open box slides across a frictionless, icy surface of a frozen lake. What happens to the speed of the box as water from a rain shower collect in it, assuming that the rain falls vertically into the box? Explain.[/b]
One might think of the slowing as being caused by the moving rear wall of the box impacting with the horizontally stationary raindrops. Kinetic energy is transferred from the box to the raindrops to get them to move with the box, slowing it down.
19 Sep 07
Originally posted by AThousandYoungGood - next question (7) to follow.
The rain will add mass to the box without adding horizontal momentum, so the box will slow down.
One might think of the slowing as being caused by the moving rear wall of the box impacting with the horizontally stationary raindrops. Kinetic energy is transferred from the box to the raindrops to get them to move with the box, slowing it down.
19 Sep 07
Originally posted by RamnedThe force of gravitational attraction F acting between two objects m1 and m2 is given by:
Law of Gravity
[b]7. If the mass of the earth were doubled at the same time as its radius were doubled, the free fall acceleration would....
A. Stay the Same. B. Decrease. C. Increase.
Explain.[/b]
F = G*m1*m2/(r^2)
The free-fall acceleration A acting on m1 is given by:
A = F/m1 = G*m2/(r^2)
If we double m2 and r, we have:
A* = G*(2*m2)/((2r)^2) = 2*G*m2/(4*r^2) = 0.5*G*m2/(r^2) = 0.5*A
Therefore, the free-fall acceleration would decrease.
19 Sep 07
Originally posted by PBE6Ditto.
The force of gravitational attraction F acting between two objects m1 and m2 is given by:
F = G*m1*m2/(r^2)
The free-fall acceleration A acting on m1 is given by:
A = F/m1 = G*m2/(r^2)
If we double m2 and r, we have:
A* = G*(2*m2)/((2r)^2) = 2*G*m2/(4*r^2) = 0.5*G*m2/(r^2) = 0.5*A
Therefore, the free-fall acceleration would decrease.
20 Sep 07
Originally posted by PBE6Good...next one to follow...
The force of gravitational attraction F acting between two objects m1 and m2 is given by:
F = G*m1*m2/(r^2)
The free-fall acceleration A acting on m1 is given by:
A = F/m1 = G*m2/(r^2)
If we double m2 and r, we have:
A* = G*(2*m2)/((2r)^2) = 2*G*m2/(4*r^2) = 0.5*G*m2/(r^2) = 0.5*A
Therefore, the free-fall acceleration would decrease.
20 Sep 07
Originally posted by RamnedConservation of angular momentum. The wheel is spinning one way but is not in contact with the Earth which would "spin" the other way (very, very slowly due to the difference in mass). Thus the motorcycle itself must spin about the axis of the rear wheel.
Rotational Dynamics
[b]8. In some motorcycle races, the riders drive over small hills so the motorcycle is airborne for some time. If the motorcycle racer keeps the throttle open while leaving the hill & going into the air, the mororcycle's nose tends to rise upwards. Why does this happen?[/b]
20 Sep 07
Originally posted by AThousandYoungIt is a conservation of angular momentum issue. Restated: Since the rear wheel is no longer in contact with the ground, it will accelerate if the throttle remains at the same position, as it has much less force countering it tangential to its surface. Viewed from the rider's left side, the force to the left that the earth exerts on the wheel is removed. This force was creating a clockwise moment on the wheel. The wheel thus gains counterclockwise momentum (wheel spins forward faster) when the bike is in the air. The total moment of the system (the bike and rider) is conserved when the nose rotates upward (clockwise moment when viewed from the left).
Conservation of angular momentum. The wheel is spinning one way but is not in contact with the Earth which would "spin" the other way (very, very slowly due to the difference in mass). Thus the motorcycle itself must spin about the axis of the rear wheel.
20 Sep 07
Originally posted by HolyTGood, well described at that. Next one to follow - may take a bit to come up with.
It is a conservation of angular momentum issue. Restated: Since the rear wheel is no longer in contact with the ground, it will accelerate if the throttle remains at the same position, as it has much less force countering it tangential to its surface. Viewed from the rider's left side, the force to the left that the earth exerts on the wheel is removed. Thi ...[text shortened]... rider) is conserved when the nose rotates upward (clockwise moment when viewed from the left).
BTW after each set of 10, I will produce a very challenging problem based on the conceptuals for each 10.
20 Sep 07
Originally posted by RamnedThanks!
Solids / Fluids
[b]9.Tornadoes and Hurricanes often lift the roofs of houses. (A) Why does this happen? Explain; use the Bernoulli Effect to explain why. (B) Why should you keep your windows open under these conditions?[/b]
The immediate physical effects of hurricanes (high straight-line winds) are far different from those of tornados (high-speed rotating winds). Forgetting the effects that I'm sure you weren't referring to, such as storm surge, hail, lightning, and rain, the common ingredient is the wind, and its effects are different for both. Can you narrow the problem down to either hurricanes or tornadoes? Or are you talking about high straight-line winds regardless of the source? I don't think you're talking about low pressure, since the pressure differences by themselves don't lift roofs.
20 Sep 07
Originally posted by RamnedIn a simplistic model the outside moving air causes a lower pressure (Bernoulli) than the inside motionless air. The pressure difference causes the building to 'explode'.
Solids / Fluids
[b]9.Tornadoes and Hurricanes often lift the roofs of houses. (A) Why does this happen? Explain; use the Bernoulli Effect to explain why. (B) Why should you keep your windows open under these conditions?[/b]
Keeping the windows open will obviously dramatically reduce the effect.