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Velocity, conservation of momentum, force, force of gravity

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1. A ball is thrown in the air with enough force so that it goes straight up for several seconds.
a. What is the velocity of the ball 1 sec before it's highest point?
b. What is the change in velocity during this 1 sec interval?
c. What is the velocity 1 sec after it reaches it's highest point?
d. what is the change in velocity during this 1 sec interval?
e. What is the change in velocity during the 2 sec interval?
f. What is the acceleration of the ball during any of these time intervals and at the moment the ball has a zero velocity?

2. An airplane is flying horizontally with speed 1000 km / h ( 280 m/s) when the engine falls off. Neglecting air resistance, if it takes 30 sec for the engine to hit the ground:
a. How high is the plane?
b. How far horizontally will the engine travel while it falls?
c. If the airplane somehow continues to fly as if nothing happened, where is the engine relative to the airplane at the moment the engine hits the ground?

3. A bicycle has wheels with a circumference of 2m. What is the linear speed of the bicycle when the wheels rotate at 1 revolution per second?

4. Before going into orbit, an astronaut has a mass of 55kg, While in orbit, a measurement determines that a force of 100N causes her to move with an acceleration of 1.90 m/s2. to regain her original weight, should she diet, or eat more?

5. A railroad car weighs four times as much as a freight car. If the railroad car coasts at 5 km/h into the freight car that is initially at rest, how fast do the two coast together after they are coupled?

6. A 60kg skydiver moving at terminal speed falls 50m in 1 sec. What power is the skydiver expending on the air?

7. To tighten a bolt, you push with a force of 80N at the end of a wrench handle that is 0.25m from the axis of the bolt:
a. What torque are you exerting?
b. If you move your hand to 0.10 from the bolt, what force do you have to exert to achieve the same torque?
c. Do your answers depend on the direction of your push relative to the direction of the wrench handle?

8. The value of g at the earth's surface is about 9.8m/s2. What is the value of g at a distance from the earth's center that is 4 times the earth's radius?

9. A 3 kg newborn at the earth's surface is gravitationally attracted to earth with a force of about 30N.
a. Calculate the force of gravity with which the baby on earth is attracted to the planet Mars, when Mars is closest to earth. (The mass of Mars is 6.4 x 1023 kg, and it's closest distance is 5.6 x 1010 meters)
b. Calculate the force of gravity between the baby and the physician who delivers it. Assume the physician has a mass of 100kg and is 0.5 m from the baby.
c. How do the forces compare?

10. Does the speed of a falling object depend on its mass? Does the speed of a satellite in orbit depend on its mass? Defend your answer.

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Solution Preview

See the attached file for the fully formatted responses.

1. A ball is thrown in the air with enough force so that it goes straight up for several seconds.
a. What is the velocity of the ball 1 sec before it's highest point?
b. What is the change in velocity during this 1 sec interval?
c. What is the velocity 1 sec after it reaches it's highest point?
d. what is the change in velocity during this 1 sec interval?
e. What is the change in velocity during the 2 sec interval?
f. What is the acceleration of the ball during any of these time intervals and at the moment the ball has a zero velocity?

Answer:

A. We know that at the highest point, the ball will have a vertical velocity of zero. Knowing that after it is released the only force acting on it is gravity, we can work backwards from this zero-velocity point to find the velocity a second earlier. Use the formula for constant acceleration:

V2 = V1 + at

0 = V1 - 9.8(1)
V1 = 9.8 m/s
Note that gravity acts downwards, while the velocity is upwards, hence the minus sign.

B. The change in velocity is obvious: the difference between the final (0 m/s) and initial (9.8 m/s) velocities.

V = -9.8 m/s (the minus sign indicates that the upward velocity decreased)

C. Following the same equation in part A. (or just looking at the same event in reverse, if you like approaching problems from a symmetry perspective), the velocity after one second will be -9.8 m/s.

D. Following part B., the change in velocity would be -9.8 m/s. Note how they are both minus - that's because gravity is acting downwards the whole time.

E. The change in velocity for the 2-second interval is simply the difference between the initial velocity (9.8 m/s upwards) and final velocity (9.8 m/s downwards, or -9.8 m/s), giving us a difference of -19.6 m/s.

2. An airplane is flying horizontally with speed 1000 km / h ( 280 m/s) when the engine falls off. Neglecting air resistance, if it takes 30 sec for the engine to hit the ground:
a. How high is the plane?
b. How far horizontally will the engine travel while it falls?
c. If the airplane somehow continues to fly as if nothing happened, where is the engine relative to the airplane at the moment the engine hits the ground?

Answer:

If the aircraft is ...

Solution Summary

Ten questions using the basics of physics understanding are addressed, including velocity, conservation of momentum, force, force of gravity.

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