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For this problem I am going to say that that onlyWhich of the following statements are true? (Mark ALL that apply.)

i. If an object receives an impulse its kinetic energy must change.

ii. An object’s kinetic energy can change without receiving any impulse.

iii. An object can receive a net impulse without any work being done on it.

iv. A force may do work on an object without delivering any impulse.

v. None of the statements above is true.

**iii**is true. To prove that the others are wrong (or to give an example), I think of a block on a table. If a force pushes down perpendicular to the table, the block won't move (no work done), but there is an impulse because there was a force exerted for a certain amount of time.

I set this up as follows:A uniform bar of unknown mass has length 40 cm. When a mass of 1 kg is hung from one end of the bar, the system will balance at a point 15 cm from the end. The mass of the bar is:

i. 4 kg ii. 1/3 kg iii. 2 kg iv. 1/2 kg v. 3 kg

[tex]\frac{5m}{8}=\frac{3m}{8}+1\implies m=4\text{kg}[/tex]

So the answer would be

**i**.

Using conservation of momentum, I come up with the daughter's final KE being 9 times the original. So answerConsider the following situation. A father and a daughter are both on roller blades in the middle of a large parking lot. They are initially skating together with a speed of 0.5 m/s. They push off of one another in such a way that the father remains stationary afterwards. The daughter weighs exactly half as much as her father. (You may assume that the daughter proceeds in the same direction after being pushed.) Which of the following statements about energy in this situation are true? (Mark ALL that apply.)

i. The final kinetic energy is twice the initial kinetic energy.

ii. Because there is no friction, kinetic energy is conserved.

iii. The final kinetic energy is less that the initial kinetic energy.

iv. The daughter’s final kinetic energy is 9 times her initial kinetic energy.

v. The father transfers his kinetic energy to the daughter.

**iv**is correct. The first choice is false (it is three times the initial), and the second and third choices are obviously false as well. The last seems false because only the momentum is transferred. I am going to say only choice

**iv**is correct.

Choice 2 seems true, because the angular velocity does not change with the radius. Three is also true by looking at the parametric equations of a cycloid (also, the direction). 4 is true because it is momentarily at rest at the bottom (as seen in a cycloid). I am going to say answer choicesA bicycle wheel rolls with speed v without slipping on a horizontal surface. Which of the following statements are true? (Mark ALL that apply.)

i. No two points on the rim of the wheel have the same speed.

ii. The angular velocity about the center is equal to the angular velocity about the contact point.

iii. No two points on the rim of the wheel have the same velocity.

iv. The velocity of the contact point is zero.

v. None of the statements above is true.

**ii**and

**iv**are true.

Thank you very much for your help .