Q1. Calculate the total momentum of two moving objects: A 1000 kg car traveling north at 15 m/s and a 2000 kg truck traveling east at 10 m/s. Find the total momentum (magnitude and direction) just before the collision.

Background

Topic: Conservation of Momentum in Two Dimensions

This question tests your understanding of how to calculate the vector sum of momenta for two objects moving in perpendicular directions. It is a classic application of the momentum vector addition in two dimensions.

Key Terms and Formulas

• Momentum ():

• Vector Addition: The total momentum is the vector sum of the individual momenta.

• Magnitude of a vector:

• Direction (angle):

Step-by-Step Guidance

1. Calculate the momentum of the car (): . The car is moving north, so its momentum is in the direction.

2. Calculate the momentum of the truck (): . The truck is moving east, so its momentum is in the direction.

3. Write the momentum components: , ; , .

4. Add the and components to get the total momentum vector: , .

5. Set up the formulas for the magnitude and direction of the total momentum, but do not calculate the final values yet.

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Q2. A 0.300 kg glider moves right at 0.80 m/s on a frictionless track and collides head-on with a stationary 0.150 kg glider. (a) Find the magnitude and direction of the final velocity of each glider if the collision is elastic. (b) Find the final kinetic energy of each glider.

Background

Topic: Elastic Collisions in One Dimension

This question tests your ability to apply conservation of momentum and kinetic energy to solve for final velocities in an elastic collision between two objects.

Key Terms and Formulas

• Conservation of Momentum:

• Conservation of Kinetic Energy:

• Elastic Collision Formulas (for and ):

Step-by-Step Guidance

1. Identify the masses and initial velocities: kg, m/s; kg, m/s.

2. Write the conservation of momentum equation for the system.

3. Write the conservation of kinetic energy equation for the system.

4. Use the elastic collision formulas to set up expressions for and .

5. Set up the kinetic energy expressions for each glider after the collision, but do not compute the final values yet.

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Q3. A 270 caliber hunting rifle fires an 8.5 g bullet at 900 m/s. (a) What impulse does the burning gunpowder impart to the bullet? (b) If it takes 2 ms for the bullet to travel the barrel, what is the average force on the bullet? (Express your answer in pounds.)

Background

Topic: Impulse and Average Force

This question tests your understanding of impulse (change in momentum) and how to relate impulse to average force over a time interval.

Key Terms and Formulas

• Impulse:

• Average Force:

• Unit Conversion: $1= 0.225$ lb (for force conversion)

Step-by-Step Guidance

1. Convert the bullet mass from grams to kilograms.

2. Calculate the impulse using (assuming the bullet starts from rest).

3. Convert the time from milliseconds to seconds.

4. Set up the formula for average force: .

5. Set up the conversion from Newtons to pounds, but do not compute the final value yet.

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Q4. Calculate the location of the center of mass of the earth–moon system (distance from the earth’s center). What can you say about the position of the center of mass with respect to the earth’s surface?

Background

Topic: Center of Mass for a Two-Body System

This question tests your ability to apply the center of mass formula to a system of two objects (Earth and Moon) and interpret the result physically.

Key Terms and Formulas

• Center of Mass (one dimension):

• Choose (Earth's center), (distance to Moon's center)

Step-by-Step Guidance

1. Identify the masses of Earth and Moon, and the distance between their centers (use data from a reference or appendix).

2. Set up the center of mass formula with and .

3. Plug in the values for , , and into the formula.

4. Interpret the result: Is the center of mass inside or outside the Earth?

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