Chapter 10 Projectile Motion & Satellite Motion

Conceptual QuestionVelma, the space woman, orbiting at 100 mi. above the earths surface, feels weightless because . . . (hint: Earth radius = 3,959 miles (6,371 km)a. she is away from the earths pull of gravityb. she is in a vacuum.c. she is falling freely around the earth.d. actually, she doesnt feel weightlesse. she went on a diet.

Conceptual Question - AnswerVelma, the space woman, orbiting at 100 mi. above the earths surface, feels weightless because . . . (hint: Earth radius = 3,959 miles (6,371 km)a. she is away from the earths pull of gravityb. she is in a vacuum.c. she is falling freely around the earth.d. actually, she doesnt feel weightlesse. she went on a diet.

Describe the motion of the ball rolling on the table.

How can you tell?

(ans to previous slide = C she is in free fall)

Describe the motion of thedropped ball.

How can you tell?

ProjectileAn object projected by some means that continues to move by its own inertia near the surface of the earth. (Only force is gravity) Examples: cannonball, baseball, rock.Usually neglect air resistance.

Projectile motionWe can think of taking a more complicated two dimensional flight and converting it into two less complicated one dimensional flights.Recall: dividing the launch velocity into a vertical and horizontal part.The horizontal component of velocity (Range) is completely independent of the vertical component (and gravity!) when air drag is small enough to ignore

Fig. 10.2

Projectile paths:Always a parabola for any launch that is not straight up.What happens if it is straight up?What type of motion is this?

Projectiles launched horizontally

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Calculating range or speed of a horizontally fired projectile (neglecting air resistance)What is the horizontal speed of the ball?

If The ball is thrown from a tower 20 m high at 40 m/s, how far will it go?

Calculating range or speed of a horizontally fired projectile (neglecting air resistance) Vertical velocity determines two crucial issues:Maximum vertical distance above the groundTime of flight (how does it do this?!!!)

10_05_Hewitt_IF.swf

Fig. 10.6The curved solid line shows the Resulting trajectory that combinesHorizontal and vertical motion.

Launching at an angle (the golf shot or bomb drop)What happens if we turn off gravity?With gravity on, the projectile falls below the ideal straight line the same amount as it would if dropped from rest. (always gt2/2 or 5t2 below the straight non-gravity path).Horizontally it moves with constant velocity (in the absence of air resistance).

Fig. 10.7The vertical distance of fall beneath the idealized straight-linePath is the same for equal times

Fig. 10.8

10_09_Hewitt_IF.swfWhat happens when we change the launch angle orlaunch velocity of a projectile?

10_11_Hewitt_IF.swf

Fig. 10.9

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2006 Pearson Education, Inc., publishing as Addison Wesley

Fig. 10.10

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2006 Pearson Education, Inc., publishing as Addison Wesley

Summary-Projectile Launched at an AngleVelocity of a projectile points along its trajectory.Vertical component changes.Horizontal component is the same everywhere.For a given angle, range increases with velocity.For a given velocity range is the same for complementary angles. Maximum range 450 (neglecting air resistance).

Orbital Motion, or . . . really fast horizontal launchIf I throw a ball horizontally (with no air resistance) it drops about __5__ m in one second. Why / How?For every 8 km(8000m) one moves horizontally, the earth drops about 5 m.I would like to throw the ball at 8000 m/s (about 17,900 mph).

Fast Moving Projectiles and Satellites

Newtons cannonIf I could fire the cannon ball with a horizontal speed of 8000 m/s what would happen?In 1 s, the ball drops 5mbut the earth curves down 5m also, so how far is the ball above the surface?The ball falls around the earth. We say it is in orbit.

10_21_Hewitt_IF.swfNewtons Cannon

Fig. 10.24

Real orbitsTo maintain our horizontal speed, we must get out of the atmosphere.The orbital speed at 100 mi above the earths surface is slightly lower, because the acceleration due to gravity is slightly less.Why? FG 1/d2

Satellite OrbitsSpeed depends on altitude (really distance from the center of the earth). As ggets smaller, v can be smaller to match the curvature of the earth.If v is bigger than necessary, the orbit is an ellipse or it escapes the planets pull.Circular Orbit: 8 km/s Elliptical Orbit: > 8 km/s < 11.2 km/sEscape Velocity: 11.2 km/sWhy does the force of gravity not change the speed and thus kinetic energy?No work done because F is perpendicular to v.

Questions:Why dont things in orbit fall?Answer?

Why are astronauts weightless?Answer?

Questions:Why dont things in orbit fall?Answer: They do! They are in free fall!

Why are astronauts weightless?Answer: They are not. They are in free fall with all their stuff!

Assignment 11Fill in the blank. (34 pnts)1.) The horizontal component of the velocity of a projectile is __________________ since the acceleration has only a __________________ component.2.) The horizontal distance a ball travels down the field is called the _____________ .3.) The vertical component of the velocity determines how _____________ the projectile goes and the ___________________ it is in the air.4.) Fill in the blank with 1/25, 1/5, same, 5 times, 25 times. Two balls are kicked off the ground so Ball Bs horizontal component is 5 times greater than Ball As and Ball Bs vertical component is the same as As. Ball Bs maximum height is ____________ Ball As. Ball B is in the air for a time that is ________________ the time that ball A is in the air.Ball Bs range is _____________ Ball As range. 5.) Fill in the blank with greater than, less than, or the same as. Each ball leaves the ground with the same initial speed. Ball A is kicked at 30 and ball B is kicked at 60. The range of A is _______________ the range of B. The height A is ___________ as the height of B. The time A is in the air is ___________ the time B is in the air.Ball A is kicked at 60 and ball B is kicked at 45. The range of A is _______________ the range of B. The height A is ___________ as the height of B. The time A is in the air is ___________ the time B is in the air.Ball A is kicked at 20 and ball B is kicked at 55. The range of A is _______________ the range of B. The height A is ___________ as the height of B. The time A is in the air is ___________ the time B is in the air.

6.) (16pnts) The acceleration due to gravity is 12 m/s2 on a given planet. (a) When a ball is dropped on this planet what is its speed at each time, how far does it fall during each interval, and how far total has it dropped. (b) Use this information to plot the location of the ball on the planet if it is thrown as shown. The strobe picture given is where the ball would be each second for the first 4 seconds if there is no gravity. Each horizontal line indicates 4 m.

speed(m/s)drop that second(m)total drop (m)00001234

** Which bullet will hit the ground first if they are simultaneously released from the same height?

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