Physics 111
Test #4 Formula Sheet
Physics 111 – Test #4
23 June 2015
Name______
Directions: This is a CLOSED BOOK test, and you may only use the calculator and cheat sheet provided. SHOW ALL OF YOUR REASONING! You can only get partial credit for an incorrect answer if you show your reasoning. You may have as much time as you like to finish this exam.
1. Consider two masses: mass A has mass 1 kg, while mass B has mass 2 kg. THE TWO MASSES HAVE THE SAME KINETIC ENERGY.
a) (5 pts) Which one (A or B) has the greater speed (or do both have the same speed)? Why?
b) (5 pts) Which one (A or B) has the greater momentum (or do both have the same momentum)? Why?
2. (6 pts) A radioactive nucleus initially at rest and experiencing zero external forces suddenly spits out an electron. The nucleus recoils. The directions the nucleus and electron move are shown below.
Must there be something else emitted at the same time the electron comes out? Why or why not?
3.The Earth has a mass of 5.97219 × 1024 kg and a radius of 6.3710 × 106 m. Its moon which has a mass of 7.3477 × 1022 kg and a radius of 1.73710 × 106 m. The distance between the centers of the Earth and the Moon is 3.84399 × 108 m.
a) (10 pts) How far above or below the Earth’s surface is the center of mass of the Earth-Moon system?
b) (5 pts) Whatexternal force(s) act on the Earth-Moon system, and what object(s) exert this (these) force(s)?
c) (5 pts) Whatinternal force(s) act on the Earth-Moon system, and what object(s) exert this (these) force(s)?
4. A 6 kg object slides without friction on a horizontal surface with a constant velocity of 12 m/s. It explodes into a 1 kg mass going 20 m/s in the same direction, and a 5 kg mass.
a. (7 pts) Determine the velocity of the 5 kg mass after the explosion.
b. (5 pts) Determine the velocity of the center of mass of the 6 kg system before AND after the explosion. How do they compare, and why? Explain. (Is this a trick question?)
c. (5 pts) Now the same thing happens only now the horizontal surface is inclined at a 20 degree angle. What are the accelerations of the center of mass of the 6 kg system before AND after the collision? Explain. (Is this a trick question?)
5. Former professionalsumo wrestler Akebono (mass = 233 kg) has decided to take figure skating lessons from Olympic silver medalist Midori Ito (mass = 40 kg). While getting up speed to perform a quadruple axel, Akebono accidentally collides with Ms. Ito. Their velocities right before the collision are shown below in the diagram. Right before and after the collision they both slide without friction on the ice. After the collision, Akebono is traveling 10 m/s at an angle of 6 degrees below the horizontal (to left).
a. (17 pts) Find Ms. Ito's velocity (magnitude and direction) right after the collision.
b. (10 pts) If the time of the collision (the length of time they are in contact) is 0.3 seconds, determine the average force (magnitude and direction) Akebono feels during the collision.
6. (20 pts) A spring with k = 444.4 N/m accelerates a 0.100 kg bouncy ball towards another bouncy ball (mass = 0.300 kg) that hangs at rest from a 1.00-meter-long string that hangs from a peg. After the collision between the two bouncy balls, the lighter one bounces backwards with a speed 1/4 what it was just before the collision. Determine the minimum initial compression of the spring in order to get the heavier bouncy ball to just barely make a circle around the peg without the string going slack. Leave your answer in cm, and assume the lighter ball just travels horizontally (it has no vertical component to its velocity when it collides). Pretend neither ball spins.
BONUS BRAIN BUSTER!!!
An open bin (box with no top) is glued to four supports that slide frictionlessly across a floor. Recall that if it is raining, the car will slow down as it fills up with water. Here, however, the car is full of water but it is not raining. Instead, the water is running out of a leak in the bottom of the car as shown in the picture (cutaway view). Will the car speed up, slow down, or keep going the same speed? Why? (Is the picture below possibly misleading?)
Credit will only be given for correct reasoning. If you are able to guess the correct answer but give no correct reasoning, you will receive no extra credit. However, if you give some correct reasoning that would (or does) lead to the correct answer, at least some credit will be given.
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By signing my name above, I affirm that this test represents my work only, without aid from outside sources. In all aspects of this course I perform with honor and integrity.