# Motion in two dimensions and gravitation, Physics and scientific inquiry

(8 points)

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**1. **During a medieval siege of a castle, the attacking army uses a trebuchet to hurl heavy stones at the castle walls. If the trebuchet launches the stones with a velocity of +30.0 m/s at an angle of 50.0°, how long does it take the stone to hit the ground? What is the maximum distance that the trebuchet can be from the castle wall to be in range? How high will the stones go? Show all your work.

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(8 points)

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**2. **A 70.0 kg astronaut is training for accelerations that he will experience upon reentry. He is placed in a centrifuge (*r* = 10.0 m) and spun at a constant angular velocity of 16.3 rpm. Answer the following:

a. What is the angular velocity of the centrifuge in rad/s?

b. What is the linear velocity of the astronaut at the outer edge of the centrifuge?

c. What is the centripetal acceleration of the astronaut at the end of the centrifuge?

d. How many *g*’s does the astronaut experience?

e. What is the centripetal force and net torque experienced by the astronaut? Give magnitudes and directions.

Show your work.

Answer:

(9 points)

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**3. **An astronaut lands on an alien planet. He places a pendulum (*L* = 0.200 m) on the surface and sets it in simple harmonic motion, as shown in this graph.

[img width=”354″ height=”253″ src=”file:///C:/Users/Spare/AppData/Local/Temp/msohtmlclip1/01/clip_image002.jpg” v_shapes=” i1025″> NUMBER 1

Answer the following questions:

a. What is the period and frequency of the pendulum’s motion?

b. How many seconds out of phase with the displacements shown would graphs of the velocity and acceleration be?

c. What is the acceleration due to gravity on the surface of the planet in m/s2? Determine the number of *g*-forces.

Show any necessary calculations.

Answer:

(8 points)

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**1. **Explain how Einstein’s contribution to understanding the force between the earth and the moon differed from Newton’s. Include a brief statement of Einstein’s explanation in your answer.

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(9 points)

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**2. **Saturn has a radius of about 9.0 earth radii, and a mass 95 times the Earth’s mass. Estimate the gravitational field on the surface of Saturn compared to that on the Earth. Show your work.

Answer:

(9 points)

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**1. **An experiment was devised to investigate the effects on the temperature of a cup of coffee when cream is added at different time intervals. Hot and cold water were used instead of coffee and cream. First, a container of water heated to 80°C was allowed to sit for 15 minutes. Its temperature was measured at regular intervals. Next, similar temperature measurements were taken for 15 minutes on a new container of heated water, but this time some cold water was added after the 2-minute reading. Finally, the procedure was repeated except that for this last test, the cold water was added after the 12-minute reading. The resulting recorded temperatures were plotted on the graph shown here.

NUMBER2

Based on the information given here, answer the following questions about the experiment.

· What question was asked in the experiment?

· What was the hypothesis, expressed as an if-then statement?

· What were the independent and dependent variables?

· What was the control in the experiment?

· Were there any sources of error in the experiment? If so, what?

· What could you conclude from the data?

Answer:

(9 points)

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**2. **Compare and contrast deductive reasoning and inductive reasoning. Based on the information given here, answer the following questions about the experiment:

· What are the qualities of deductive reasoning?

· What are the qualities of inductive reasoning?

· Throughout the history of physics, when did these types of reasoning come into play?

· Provide one example of a physicist who used deductive reasoning, one who used inductive reasoning, or one who used both.

Answer:

(7 points)

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**3. **The data in Light-Duty Vehicles (1975–2006) show the efficiency of light-duty vehicles from 1975 (leftmost point of the connected line) to 2006 (rightmost point of the connected line). Each point represents a year in chronological order from the left end to the right.

Data adapted from http://www.sightline.org/images/blog-2008/Mileage-horsepower-EPA-600.gif

NUMBER3

Look at the graph carefully and answer the following questions:

· What generalizations can you make about changes in fuel efficiency (miles per gallon, MPG) over the course of the study?

· What generalizations can you make about changes in engine performance (horsepower) over the course of the study?

· What generalizations can you make about changes in vehicle efficiency (horsepower multiplied by MPG) over the course of the study?

Answer: