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... of objects in 3-D under constant acceleration (problem in projectile motion) ... If projectile begins and ends at same height, maximum distance is achieved for Q ...
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## projectile

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Title: Announcements: 1 Announcements
• Physics Learning Resource Center Open,
• gt room P207-C
• Open 9am - 5 pm Monday - Friday
• Hours also listed on www.phys.uconn.edu
• NOTE
• Homework 1 (due this Fri. 9/8 by 500 pm EST on WebAssign)
• Homework 2 (due next Fri. 9/15 by 5.00 pm)
• 2 Physics 151 Lecture 5Todays Agenda(Chapter 4)
• Projectile motion
• Uniform circular motion
• text sections 4.1-4.5
• 3 ACT -1Question from past Exam-1 Two balls, projected at different times so they dont collide, have trajectories A and B, as shown.
• Which statement is true.
• Initial speed of ball B must be greater than that of ball A.
• Ball A is in the air for a longer time than ball B.
• Ball B is in the air for a longer time than ball A.
• Ball B has a greater acceleration than ball A.
• None of above.
• 4 Review Kinematics in 3D (2D)
• Motion of objects in 3-D under constant acceleration (problem in projectile motion)
• -gt independence of x- and y- components y y0 v0y t - 1/ 2 g t2 vy v0y - g t ? to 0 Animation (v) Animation (a) x vx t vx v0x 5 Review Kinematics in 3D (2D) (cont.)
• How many parameter determine projectile motion ?
• at to 0 xo, yo , vox, voy we have 4 equations ! 9 variables plus ag at t t x(t) , y(t), vx, vy 4 independent variables ! 6 Projectile Motion g v0 Q Typical Questions, 1. Dx How far will it go ? 2. Dy How high will it be at some distance ? 3. t How long until it hits ? 4. Q At what angle should I start ? 5. v0 How fast must I start ? 7 Projectile Motion g v0 Q
• Useful Things to Know
• If projectile begins and ends at same height, maximum distance is achieved for Q 45. (prove it)
• x distance is same for angles about 45 if everything else remains the same.
• Time in flight depends on y equation if no barriers other than the earth interrupt the flight path.
• 8 Projectile Motion / Example Problem v0 g Q UConn football team wants to complete a 45m pass (about 50 yards). Our qb can throw the ball at 30 m/s. At what angle must he throw the ball to get it there ? SOLUTION Q 15 or 75 which gets there first ? 9 Problem 3 (correlated motion of 2 objects in 3-D)
• Suppose a projectile is aimed at a target at rest somewhere above the ground as shown in Fig. below. At the same time that the projectile leaves the cannon the target falls toward ground.
• t t1 10 Review( displacement, velocity, acceleration ) Velocity Acceleration 11 General 3-D motion with non-zero acceleration because either or both Animation
• Uniform Circular Motion is one specific case of this
• 12 Uniform Circular Motion See text 4-4
• What does it mean ?
• How do we describe it ?
• What can we learn about it ?
• 13 What is Uniform Circular Motion (UCM) ? See text 4-4
• Motion in a circle with
• Constant Speed v v
• acceleration ?
• 14 How can we describe UCM? See text 4-4
• In general, one coordinate system is as good as any other
• Cartesian
• (x,y) position
• (vx ,vy) velocity
• Polar
• (R,?) position
• (vR ,?) velocity
• In UCM
• R is constant (hence vR 0).
• ? (angular velocity) is constant.
• Polar coordinates are a natural way to describe UCM!
• y v (x,y) R ? x 15 Polar Coordinates See text 4-4
• The arc length s (distance along the circumference) is related to the angle in a simple way
• s R?, where ? is the angular displacement.
• units of ? are called radians.
• For one complete revolution
• 2?R R?c
• ?c 2?
• ??has period 2?.
• 16 Polar Coordinates...
• In Cartesian co-ordinates we say velocity dx/dt v.
• x vt
• In polar coordinates, angular velocity d?/dt ?.
• ? ?t
• ? has units of radians/second.
• Displacement s vt.
• but s R? R?t, so
• y v R s ???t x 17 Period and Frequency
• Recall that 1 revolution 2? radians
• frequency (f) revolutions / second (a)
• angular velocity (?) radians / second (b)
• By combining (a) and (b)
• ? 2? f
• Realize that
• period (T) seconds / revolution
• So T 1 / f 2?/?
• 18 Lecture 5, ACT 2Uniform Circular Motion
• A fighter pilot flying in a circular turn will pass out if the centripetal acceleration he experiences is more than about 9 times the acceleration of gravity g. If his F18 is moving with a speed of 300 m/s, what is the approximate diameter of the tightest turn this pilot can make and survive to tell about it ?
• 19 Acceleration in UCM
• This is called Centripetal Acceleration.
• Now lets calculate the magnitude
• But ?R v?t for small ?t 20 Lecture 5, ACT 2Uniform Circular Motion
• A fighter pilot flying in a circular turn will pass out if the centripetal acceleration he experiences is more than about 9 times the acceleration of gravity g. If his F18 is moving with a speed of 300 m/s, what is the approximate diameter of the tightest turn this pilot can make and survive to tell about it ?
• (a) 20 m
• (b) 200 m
• (c) 2000 m
• (d) 20,000 m
• 21 Recap for today
• Recap of Projectile Motion
• Introduce Uniform Circular Motion
• Reread Circular Motion Ch 4.4-4, pp.91-95
• Read Relative Velocity Ch 4.5, pp.95-99
• Homework 1 (due this Fri. 9/8 by 500 pm EST on WebAssign) Problems from Chapter 1 and 2
• Homework 2 (due next Fri. 9/15 by 5.00 pm)
• Problems from Chapter 3 and 4
• Recommended

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#### Uniform Circular Motion 