Physics H131: Problem Set #2

Two-Minute/Short-Answer Problems

Remember to give a good explanation, no longer than two sentences.

• C3T.3: What does the momentum transfer principle predict if the second cart is "free", i.e. not involved in another interaction except for the collision itself?
• C3T.8: Which momentum component is affected by the gravitational interaction? What does this imply for the components of the velocity vector?

Chapter C2 Problems

Remember to always include the correct units with dimensionful numbers! Remember that each component of a vector has the same units as the vector as a whole or as its magnitude.

• C2S.5: Use a standard reference frame with the airport at the origin. Translate the data given in the problem into a displacement vector relative to the origin. Compute its magnitude and the requested angles using trigonometry. Draw a sketch of the situation to make sure you use the correct trigonometric relations!
• C2R.2: Choose a reference frame (don't forget to tell me about your choice!) and translate the data given in the problem into vector notation, with components specified in your reference frame. Think about a strategy how to answer the question and write down the strategy. Then execute it. How can you determine the distance between the two teams at their night camps? Think three-dimensionally!

Chapter C3 Problems

• C3B.2: Be careful to avoid the trap of dividing by a vector (which is meaningless)! What should you do first, before solving for the time interval?
• C3B.5: Use the momentum transfer principle. What is the cart's initial momentum? The "impulse" is the momentum transferred in the collision, during the very short time interval dt of the collision process. Given he initial momentum and the impulse, how can you get the final velocity? Think about how velocity and momentum are related. Keep careful track of the directions of the vectors involved.
• C3S.3: Going directly to the diagram C3.5c for this process may be a little tricky. Think first about the following questions: How many objects are moving before the collision, and how many are moving afterwards? You can consider the carts after the collision as a single object with a different mass, or as two objects with their original masses which now must move with the same velocity. Either way is ok. How can you use the fact that momentum is only transferred but not lost to determine the final velocity of the two carts stuck together? If the two carts must move with the same velocity after the collision, what does this imply for the momentum transferred to each cart in the collision?
• C3S.4: How is "force" defined? Where is the information given which allows you to connect the gravitational downward impulse with the gravitational force? How is the gravitational force acting on the book related to its mass? Is the book's state of motion changed by the gravitational impulse it keeps receiving? What does the answer to this question tell you?
• C3R.1: In this problem you can make your life very hard or very easy depending on your choice of reference frame. Remember that moving reference frames are ok - after all, even the standard reference frame is moving around the center of the earth with the earth's rotation and with the earth around the sun. Think about whether all the data given in the problem are relevant for answering the question. Do you really need to know how fast your own plane is moving, and in which direction? Why? Draw a vector diagram representing the two "observations" made by you about the other plane. Is it really important that the observations were made 30 seconds apart? Why?