10/30/15 Oregon State University PH 211, Class #15 1

A baseball (0.250 kg) is struck by a bat and leaves it at a 35° angle (above the horizontal) at a speed of 40 m/s. Find the magnitude of the net force on this projectile when it is 1.46 seconds into its flight.

1. 0.00 N

2. 2.45 N

3. 8.19 N

4. 10.0 N

5. None of the above.

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A 150,000 kg jet airliner is moving with constant velocity at an angle of 12.7° above the horizontal, at an altitude of 10 km and a speed of 200 m/s. What is magnitude of the total force acting on the airplane?

1. 0.00 N

2. 1.43 x 106 N

3. 1.47 x 106 N

4. There is not enough information.

5. None of the above.

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Local Gravity, Local FG

Any mass as large as a planet exerts a significant force on any other mass—such as you. If you let that be the net force—the only force acting on you (i.e. you step off a roof)—you know what happens: That net force causes you to accelerate. And we have measured the local magnitude of that acceleration here on the earth’s surface: g

But Newton’s Second Law says that every net force Fnet causes a body to accelerate according to Fnet = ma. So the force by gravity on you—is given by FG = mg.

Of course, on other planets, the local gravitational acceleration value is different—depending on the characteristics of that planet. So, to find the local gravitational force on any object, you must use its mass and the local value of gravitational acceleration.

Weight

What is it? Weight is a force—a vector quantity—measured in pounds (English), newtons (SI), dynes, ounces, tons, etc…

What does it measure? Your weight is the negative of the sum of all contact forces acting on you (i.e. all forces except gravity). Your weight can be indicated typically by a scale upon which you stand, sit, or hang.

What factors affect any object’s weight? Its mass, its location, and its reference frame. Weight is proportional to g and m.

Example: For a non-accelerating object near a planet:

weight = mg = FG

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The local gravitational acceleration on the moon’s surface is about 1/6 that on the earth’s surface.

(a) Find the weight of a 12.0-kg block at rest on the moon’s surface.

(b) If you have a level, frictionless table on the moon, and you push on the above block with a constant horizontal force of 60.0 N, predict the magnitude of that block’s horizontal acceleration.

1. (a) 2.0 N (b) 5.00 m/s2

2. (a) 2.0 N (b) 0.833 m/s2

3. (a) 19.6 N (b) 5.00 m/s2

4. (a) 19.6 N (b) 30.0 m/s2

5. None of the above.

Your weight in an elevator

An 80 kg man stands on a scale in an elevator that is stationary. What is his weight (the reading on the scale)? Let g = 10 m/s2.An 80 kg man stands on a scale in an elevator that is accelerating upward at 2 m/s2. What is his weight?An 80 kg man stands on a scale in an elevator that is accelerating downward at 2 m/s2. What is his weight?An 80 kg man stands on a scale in an elevator that is moving upward at a constant 5 m/s. What is his weight?An 80 kg man is in an elevator with broken cables and brakes—it’s plummeting downward in freefall.What is his weight?

 

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Weightlessness

A person can be weightless in a location with no gravity. (Where would that be?) But a person in a state of freefall is also weightless. Even if a scale is present, it won’t push/pull on you if you’re in freefall.

But notice: For an object in freefall, gravity is clearly still present! FG is not zero in this case.

So how/why are astronauts weightless when in orbit around the earth?

 

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Orbital Motion and Gravity:Newton’s Thought Experiment

A cannon on a mountaintop fires a shell parallel to the ground. The shell leaves the cannon and is thereafter pulled toward the ground by gravity.

If the shell leaves the cannon with a low velocity, it falls to the ground near the mountain.With a higher velocity, it falls farther from the mountain.

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So, what if the shell is traveling so fast, that for every foot it falls, the Earth also curves away from it by one foot? The shell will be forever falling—never landing. It will be in orbit!

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Being in orbit is being in a state of freefall.The Moon, in orbit, is forever “falling” to the Earth. Likewise, astronauts in orbit are in freefall, and are thus in a state of weightlessness.

The same is true for any planet, moon, comet, asteroid, or other satellite in orbit around any other body.

YES. There’s still strong gravity for the astronauts in orbit. Otherwise the spacecraft wouldn’t stay in orbit. At the altitude of the space shuttle’s orbit, for example, the strength of gravity is about 90% of that on the earth’s surface: gorbit ≈ 8.7 m/s2

Gravity for spacecraft in orbit?

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Newton’s Laws are often misquoted, misunderstood and misapplied.

Consider the cautionary tale of Sir Edward Horse…