Physics 101 Homework

Physics 125 Test 2 Apr. 2, 2020 Name: Part 1: Below are 6 short work out questions. Answer any 5 of the 6 questions. YOU MUST SHOW ALL YOUR WORK TO RECEIVE ANY CREDIT. You may do the remaining question as a bonus. Indicate which questions are to be graded and which is the bonus. 1. a) A bomb is moving to the right at 0.3 c. Ship A is chasing the bomb at 0.5 c to the right while ship B is chasing the bomb at 0.5 c to the left. Which ship, A or B, will measure the largest dilated time for the bomb to explode? Explain your reasoning.

b) Three equal mass objects are each acted upon by different forces acting in the x-direction. The x-velocity as a function of time for each mass is shown below. Rank the forces in the x- direction acting on each of the masses from smallest to largest. Note any ties.

c) Mass m is at rest on an inclined plane. The coefficient of static friction between the mass and the inclined plane is 𝜇". Student A claims that the static frictional force acting on m is equal to 𝜇"𝑁. Student B claims that the static frictional force acting on m is equal to 𝑚𝑔𝑠𝑖𝑛𝜃. Student C claims that the static frictional force acting on m must exceed the x-component of the weight. Which student is correct? Explain your reasoning.

d) Mass m is swung in a vertical circle of radius R. Rank the tensions in the string at points A, B, and C from least to greatest assuming that the speed is a constant. Do not neglect gravity.

2. Find an expression for the acceleration of the masses. Your answer should only contain 𝑚*, 𝑚+, 𝜇, and various constants.

a =

3. Masses 𝑚* and 𝑚+ are connected by a string, which passes over a frictionless and massless pulley. Mass 𝑚* is at rest on an inclined plane. The coefficient of static friction between mass 𝑚* and the inclined plane is 𝜇". What is maximum value that 𝑚+ can have before 𝑚* starts to move? Your answer will be in the form of an expression.

𝑚+-./ =

4. A car of mass m is traveling over a series of hills and valleys. The hills and valleys can be viewed as hemispheres of radius R. a) If the car on top of the hill, point A, just loses contact with the road, what must be the car’s speeds. You answer will be in the form of an equation. b) If the car’s speed does not change from part a), what will be the normal force acting on the car at point B? You answer will be in the form of an equation.

v at point A = N =

5. You are traveling in space ship A. You measure the length of ship A to be 200 m. You see space ship B coming towards you with a speed of 0.99c. You measure the length of B’s ship to also be 200 m. a) What is the length of ship B according to someone traveling on ship B? b) What is the length of ship A as measured by someone on ship B?

6. A ball is thrown straight upwards with an initial velocity of 𝑣2. Assuming that the air resistance is given by 𝐹.4 = 𝑏𝑣 where 𝑏 is a constant, prove that the velocity of the ball as a function of time is given by

𝑣(𝑡) = :-; < + 𝑣2>𝑒

@AB C − -;

< .

Take up to be positive. Hint: Start with the free body diagram. Also, how do you think that you are going to write the acceleration?

Part 2: Below are 3 longer work out questions. YOU MUST SHOW ALL YOUR WORK TO RECEIVE ANY CREDIT. Answer all 3 questions. 1. An astronomer on earth discovers planet X 100 ly away from the earth. Earth sends out a ship, which travels at 0.85 c, towards the planet. The inhabitants of planet X shoot a missile at the earth ship. The speed of the missile is 0.9 c.

a) What is the distance between earth and planet X according to someone on the earth ship? What is the distance between earth and planet X according to someone riding on the missile? distance according to someone on the earth = ship distance according to someone on the missile =

b) What is the velocity of the missile according to someone on the ship from earth? velocity of the missile according to someone of the earth ship = c) Someone on the earth ship sees that the missile self destructs in 2 hours. How long would it take the missile to self destruct according to someone on the missile? time it takes the missile to self destruct according to someone = on the missile

2. Consider the three masses connected as shown below. The inclined plane make an angle q with the horizontal. The coefficient of kinetic friction on all surfaces is 𝜇,. The pulleys are massless and frictionless. The masses move as shown below.

a) Draw the free body diagrams for each mass.

b) Apply Newton's second law to each of the masses. DO NOT solve the equations yet. Just set them up. c) Using your equations, derive an expression for the acceleration. Your answer should only contain 𝑚*, 𝑚+, 𝑚E, 𝜇,, , and various constants.

3. Two equal mass 1 kg balls are connected by strings and swung in horizontal circles. The radii of the circles and the angles that the strings make with the vertical are shown below. Answer the following questions. Do not neglect gravity.

a) Draw the free body diagram of mass 1 and find the tension in string 1. b) What is the velocity of mass 1?

c) Draw the free body diagram of mass 2 and find the tension in the string 2. b) What is the velocity of mass 2?