PHY, Ch.10- Homework

Video: Projectile Motion Part A- When Dr. Hewitt releases the two projectiles, which one hits the ground first?

Both balls hit the ground at the same time.

Video Tutor: Ball Fired Upward from Accelerating Cart. Part A- Consider the video you just watched. Suppose we replaced the original launcher with one that fires the ball upward at twice the speed. We make no other changes. How far behind the cart will the ball land, compared to the distance in the original experiment?

Four times as far. The ball will spend twice as much time in the air (t=2voy/g, where voy is the ball's initial upward velocity). When subtracting the horizontal distance the cart travels in time, t, from the horizontal distance the ball travels in time, t, the term involving initial velocity of the cart (which is also the horizontal velocity of the ball) cancels out, leaving only d=1/2 axt^2 (where ax is the cart's horizontal acceleration). The ball will land four times further behind.

Video: Projectile Motion Part B- When Dr. Hewitt releases the two objects, how can we tell whether one of the objects hits the ground first or whether they both hit at the same time?

We are able to hear the two balls fall.

Think and Solve 10.26 A ball is thrown horizontally from a cliff at a speed of 10m/s. You predict that its speed 1 s later will be slightly greater than 14 m/s. Your friend says it will be 10 m/s. Part A- Who is correct?

You

Prelecture Reading Question 10.06 Part A- For an Earth Satellite in an elliptical orbit, list all the values that do not change.

Speed, gravitational force, and distance from Earth.

Reading Check 10.23 Part A- What is the ratio of escape speed from Earth to circular orbit speed? Ignore air resistance.

1.41

Video: Projectile Motion Part C- Why do the two objects hit the table at the relative times that they do?

Gravity pulls the same amount on both, and they both drop the same distance.

Reading Check 10.17 Part A- At what part of an elliptical orbit does an Earth satellite have the greatest speed? The lowest speed?

Greatest nearest Earth; lowest further from Earth.

Think and Solve 10.27 You're in an airplane that flies horizontally with speed 830 km/h (230 m/s) when an engine falls off. Neglecting air resistance, assume it takes 30 s for the engine to hit the ground. Part A- Find the height of the airplane.

H= 4.4 km

Video: Velocity during Projectile Motion. Part B- Predict how the vertical component of the velocity will change with time after the projectile is fired.

It first decreases to zero and then increases in the opposite direction.

Reading Check 10.09 Part A- How can a projectile "fall around the Earth?"

-The projectile falls 5 m for every 8 km and so does Earth. -A projectile can "fall around Earth" if the distance it falls matches the curvature of Earth -In a circular orbit around a spherical planet, the force and the fall are always toward the center.

Prelecture Reading 10.10 Part A- Escape speed from Earth is any speed equal to or greater than

11.2 km/s

Reading Check 10.05 Part A- A projectile falls beneath the straight-line path it would follow if there were no gravity. How many meters does it fall below this line if it has been traveling for 1s? For 2s?

5m, 20 m

Video: Velocity during Projectile Motion. Part A- Predict how the horizontal component of the velocity will change with time after the projectile is fired.

It stays constant.

Video Tutor: Dropped and Thrown Balls. Part A- Which ball (if either) has the greatest speed at the moment of impact?

The ball thrown horizontally. The two balls have the same vertical velocity when they land, but the thrown ball has an additional horizontal velocity component. Since speed is defined as the magnitude of the resultant velocity vector, the thrown ball is moving faster when it lands.

Think and Discuss 10.100 Part A- A rocket coasts in an elliptical orbit around Earth. To attain the greatest amount of KE for escape using a given amount of fuel, should it fire its engines to accelerate forward when it is at the apogee or at the perigee? (Hint: Let the formula Fd=Δ KE be your guide to thinking. Suppose the thrust F is brief and of the same duration in either case. Then consider the distance d the rocket would travel during this brief burst at the apogee and at the perigee.)

At the perigee.

Think and Discuss 10.90 A communication satellite with a 24 hour period hovers over a fixed point on Earth, and, to Earth observers, seems motionless. Part A- Why is it placed only in an orbit in the plane of the Earth's equator? Think of the satellite's orbit as a ring around Earth.

In order to appear motionless to an observer at a fixed location on Earth's surface, the satellite must rotate around Earth at the same [rate as Earth rotates around its own axis] and both the location and satellite must be in [the same line between Earth's center and the satellite] This can only occur above Earth's equator. Above any other location, the "ring" of satellite motion and the "ring" of motion of the location on Earth's surface [would not] be in the same place.

Think and Explain 10.69 Part A- Can a satellite coast in a stable orbit in a plane that doesn't intersect the Earth's center? Defend your answer.

No way, for the Earth's center is a focus of the elliptical path (including the special case of a circle), so an Earth satellite orbits the center of the Earth. The plane of a satellite coasting in orbit always intersects the Earth's center.

Prelecture Reading Question 10.05 Part A- For an Earth satellite in circular orbit, list all the values that do not change.

Only speed, gravitational force, and distance from Earth.

Think and Discuss 10.99 Part A- A giant rotating wheel in space provides artificial gravity for its occupants as discussed in Chapter 8 in the textbook. Instead of a full wheel, discuss the idea of a pair of capsules joined by a tether line and rotating about each other. Can such an arrangement provide artificial gravity for the occupants?

The design is a good one. Rotation would provide a centripetal force on the occupants. Watch for this design in future space habitats.

Reading Check 10.13 Part A- Why does the force of gravity change the speed of a satellite in circular orbit?

The force is at a right angle to the velocity.

Reading Check 10.21 Part A- Why is kinetic energy a constant for a satellite in a circular orbit but not for a satellite in an elliptical orbit?

The force of gravity is perpendicular to the motion in a circular orbit but not in an elliptical orbit.

Think and Solve 10.27 You're in an airplane that flies horizontally with speed 830 km/h (230 m/s) when an engine falls off. Neglecting air resistance, assume it takes 30 s for the engine to hit the ground. Part B-Find the horizontal distance that the aircraft engine falls

d= 6.9 km

Think and Solve 10.27 You're in an airplane that flies horizontally with speed 830 km/h (230 m/s) when an engine falls off. Neglecting air resistance, assume it takes 30 s for the engine to hit the ground. Part C- If the airplane somehow continues to fly as if nothing had happened, what is the distance between the engine and the airplane at the moment the engine hits the ground?

d=4.4 km