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Physics 103: Lecture 6 2D Motion + Relative Velocities

Physics 103: Lecture 6 2D Motion + Relative Velocities. Today’s lecture will be on More on 2D motion Addition of velocities Start Newton’s laws: first law. Dart hits the. monkey!. Shooting the Monkey. y = y 0 - 1 / 2 g t 2. At an angle, still aim at the monkey!.

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Physics 103: Lecture 6 2D Motion + Relative Velocities

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  1. Physics 103: Lecture 62D Motion + Relative Velocities • Today’s lecture will be on • More on 2D motion • Addition of velocities • Start Newton’s laws: first law Physics 103, Fall 2009, U.Wisconsin

  2. Dart hits the monkey! Shooting the Monkey... y= y0 - 1/2 g t2 • At an angle, still aim at the monkey! y= vy0t - 1/2 g t2 g = 9.8 Physics 103, Fall 2009, U.Wisconsin

  3. Review: 2D Motion • y = y0 + v0yt + 1/2 ayt2 • vy = v0y +ayt • vy2 = v0y2 + 2ayy • x = x0 + v0xt + 1/2 axt2 • vx = v0x +axt • vx2 = v0x2 + 2axx • Solving 2D motion problems • Make a pictures and write out the equations • Mark everything you know and what you want to know • Simplify, eliminate 0 terms • Think, is there an obvious answer to the problem? • Shoot the Monkey: The dart would hit the monkey without gravity so if you add the same gravity term to both the dart will still hit the target • Solve remembering time is in both sets of equations Physics 103, Fall 2009, U.Wisconsin

  4. Summary Projectile Motion • y = y0 + v0yt - 1/2 gt2 • vy = v0y -gt • vy2 = v0y2 - 2g y • x = x0 + v0t • v = v0x Physics 103, Fall 2009, U.Wisconsin

  5. Reference Frames: Relative Motion VBC=VBA+VAC Velocity of B relative to ground ( C ) : VBC Velocity of A relative to ground ( C ) : VAC Velocity of B relative to A : BA Physics 103, Fall 2009, U.Wisconsin

  6. Relative Motion • If an airplane flies in a jet stream, depending on the relative orientation of the airplane and the jet stream, the plane can go faster or slower than it normally would in the absence of the jet stream • If a person rows a boat across a rapidly flowing river and tries to head directly for the shore, the boat moves diagonally relative to the shore • Velocity is a vector - add velocities like vectors • Sum the components • Vx = V1x + V2x • V1x = V1 cosq, V2x = V2 cosq2 • Vx = V1 cosqV2 cosq • Vy = V1y + V2y • V1y = V1 sinq, V2y = V2singq2 • Vy = V1 sinq V2 sinq Physics 103, Fall 2009, U.Wisconsin

  7. correct Lecture 5, Pre-Flight 5 and 6 A seagull flies through the air with a velocity of 9 m/s if there were no wind. However, it is making the same effort and flying in a headwind. If it takes the bird 20 minutes to travel 6 km as measured on the earth, what is the velocity of the wind? 1. 4 m/s 2. -4 m/s 3. 13 m/s 4. -13 m/s • Seagull’s velocity relative to the wind = 9 m/s • i. e., in the frame relative to the wind, wind velocity is zero • Seagull travels at 6000/1200 = 5 m/s relative to earth. Therefore, the wind velocity relative to earth is 5-9=-4 m/s. Physics 103, Fall 2009, U.Wisconsin

  8. correct Follow-up, Pre-Flight 5 and 6 If the seagull turns around and flies back how long will it take to return? 1. More time than for flying out 2. Less time than for flying out 3. The same amount of time • Seagull’s return velocity is: -4-9=-13 m/s. The speed is higher so it takes less time to return. Time taken for the return is given by 6000 m / 13 (m/s) = 461.5 s = 461.5/60 = 7.69 minutes Physics 103, Fall 2009, U.Wisconsin

  9. correct Pre-Flight Follow up A seagull is flying at 9m/s and covers 6.00km to an island and back. How are the rounds-trip times with and without a 4.00m/s wind related if the seagull always goes at 9.00 m/s relative to the wind? 1. The round-trip time is the same with/without the wind 2. The round trip time is always larger with the wind 3. It is not possible to calculate this • Time taken for the round trip without wind is: 12000 m / 9 m/s = 1333 s = 22.2 minutes • Time taken for the round trip with wind is: 27.7 minutes • Always calculate your relative velocities first and then apply standard equations. Think about the answer, does it make sense? Physics 103, Fall 2009, U.Wisconsin

  10. correct ABC Lecture Pre-Flight Three swimmers can swim equally fast relative to the water. They have a race to see who can swim across a river in the least time. Relative to the water, Beth (B) swims perpendicular to the flow, Ann (A) swims upstream, and Carly (C) swims downstream. Which swimmer wins the race? A) Ann B) Beth C) Carly Physics 103, Fall 2009, U.Wisconsin

  11. ABC Lecture Pre-Flight • Beth will reach the shore first because the vertical component of her velocity is greater than that of the other swimmers. • The key here is how fast the vector in the vertical direction is. "B" focuses all of its speed on the vertical vector, while the others divert some of their speed to the horizontal vectors. Time to get across = width of river/vertical component of velocity Physics 103, Fall 2009, U.Wisconsin

  12. Newton’s First Law • The motion of an object does not change unless it is acted upon by a net force. • If v=0, it remains 0 • If v is some value, it stays at that value • Another way to say the same thing: • No net force  • velocity is constant • acceleration is zero • If there is a net force  • velocity will change • acceleration is not zero Physics 103, Fall 2009, U.Wisconsin

  13. Contact and Field Forces Physics 103, Fall 2009, U.Wisconsin

  14. The Four Forces • Types • Strong nuclear force • Electromagnetic force • Weak nuclear force • Gravity • Characteristics • All field forces • Listed in order of decreasing strength • Only gravity and electromagnetic forces are relevant in classical mechanics, which deals with motion of macroscopic objects. Physics 103, Fall 2009, U.Wisconsin

  15. lift drag thrust weight Net Force When the velocity is constant the objects acceleration is equal to zero. The only time acceleration is equal to zero is when the sum of the net force is equal to zero. Net force is 0 An object traveling at a constant velocity along a straight line will continue to do so as long as there is no net force acting on it (Newton's First Law). The total force acting on the plane is zero, because its motion is constant in a straight line. Physics 103, Fall 2009, U.Wisconsin

  16. An object is held in place by friction on an inclined surface. The angle of inclination is increased until the object starts moving. If the surface is kept at this angle, the object 1. slows down 2. moves at uniform speed 3. speeds up 4. none of the above When the object is at rest net force on it is zero. When the object starts to move there is change in velocity - i.e., there is acceleration or a net force due to gravity The force remains constant when inclination is kept at that angle leading to constant acceleration - continuous speed up. Physics 103, Fall 2009, U.Wisconsin

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