Conceptual Physics Energy Sources Collisions

Transcription

1 Conceptual Physics Energy ources Collisions Lana heridan De Anza College July 7, 2015

2 Last time energy and work kinetic energy potential energy conservation of energy energy transfer simple machines efficiency

3 Overview discussion of energy sources momentum and collisions

4 ources of Energy Discussion!

5 ources of Energy ources of energy: oil coal natural gas wood / charcoal / peat solar - photovoltaics and heating wind waves hydroelectric geothermal nuclear - thermonuclear, fission, and fusion(?)

6 ources of Energy: Fraction of U Energy supply 1 U Energy Information Administration.

7 ources of Energy: Costs 1 Wikipedia, NEA estimates.

8 ources of Energy: Costs 1 Wikipedia, California Energy Commission estimates.

9 Carbon Dioxide 1 Graph from

10 Collisions The conservation of momentum is very useful when analyzing what happens to colliding objects. In all collisions (with no external forces) momentum is conserved: net momentum before collision = net momentum after collision p net,i = p net,f

11 Types of Collision There are two different types of collisions: Elastic collisions are collisions in which none of the kinetic energy of the colliding objects is lost. (K i = K f )

12 Types of Collision There are two different types of collisions: Elastic collisions are collisions in which none of the kinetic energy of the colliding objects is lost. (K i = K f ) Inelastic collisions are collisions in which energy is lost as sound, heat, or in deformations of the colliding objects.

13 Types of Collision There are two different types of collisions: Elastic collisions are collisions in which none of the kinetic energy of the colliding objects is lost. (K i = K f ) Inelastic collisions are collisions in which energy is lost as sound, heat, or in deformations of the colliding objects. When the colliding objects stick together afterwards the collision is perfectly inelastic.

14 Elastic Collisions m 1 m 2 a Before the collision, the particles move separately. v1f v1i v2i After the collision, the particles continue to move separately m 1 with new velocities. m 2 a v1f v2f After the collision, the b particles continue to move separately with new velocities. Figure 9.7 chematic representation of an elastic head-on colli- v2f ties, and Because alternativ represente tion of E direction. factor 1 W 2 i tive left if and it mo2 In a typ ties, and E alternative tion Factoring of Equ factor 1 2 in left and 2 o Next, lar way to Factoring b

15 Example: Pool A pool ball moving at 1 m/s to the right strikes a stationary pool ball in an elastic collision. What is the final velocity of the two pool balls? (Assume they have the same mass.) 1 Photo by Max tansell via hsphysicslab.blogspot.com.

16 Example: Pool A pool ball moving at 1 m/s to the right strikes a stationary pool ball in an elastic collision. What is the final velocity of the two pool balls? (Assume they have the same mass.) The motional energy is just transferred from the first ball to the second! The first ball comes to rest after the collision, and the second moves off to the right at 1 m/s. Notice that momentum is conserved. 1 Photo by Max tansell via hsphysicslab.blogspot.com.

17 Inelastic Collisions For general inelastic collisions, some kinetic energy is lost. But we can still use the conservation of momentum: p i = p f

18 sion, we can ntum Perfectly of the Inelastic Collisions a (9.15) (9.14) 1 m Before the collision, the 2 particles move separately. After the m vcollision, 1i vthe 2i particles 1 move together. and v a 2i (9.15) articles v 1f and v After the collision, f the system particles m 1 move m 2 together. s tion v 1i and in v 2i b wo particles velocity! ties, v 1f and Figure 9.6 chematic representation of a perfectly m 1 m 2 inelastic v f f the (9.16) system direction in head-on collision between two b (9.17) particles. Now the two particles stick together after colliding same final m2 p i = p f m 1 v 1i + m 2 v 2i = (m 1 + m 2 )v f

19 Inelastic Collision Example From page of Hewitt: Two freight rail cars collide and lock together. Initially, one is moving at 10 m/s and the other is at rest. Both have the same mass. What is their final velocity?

20 Collision Question Two objects collide and move apart after the collision. Could the collision be inelastic? (A) Yes. (B) No.

21 Question In a perfectly inelastic one-dimensional collision between two moving objects, what condition alone is necessary so that the final kinetic energy of the system is zero after the collision? (A) The objects must have initial momenta with the same magnitude but opposite directions. (B) The objects must have the same mass. (C) The objects must have the same initial velocity. (D) The objects must have the same initial speed, with velocity vectors in opposite directions. 1 erway & Jewett, page 259, Quick Quiz 9.5.

22 600 N/m numerical values: served when t v 1i implies that th m important sub 1 Finalize This answer is not the maximum compression of the spring because iar example the two in m each other at the instant shown in Figure 9.10b. Can you determine 2 the surface. maximum For com su a for conservatio x m More Complicated Collisions As an example, consider the case of a glancing collision. a Before the collision v 1i m 1 m 2 After the collision v 1f sin θ φ v2f sinφ v 2f cos φ After the collision 9.5 Collisions in Two Dimension In ection 9.2, we v 1f sin showed θ that the momentum where the thr of served when the system is isolated. sent, For any respectiv collis implies that the momentum v 1f cos in θeach and of the the directi veloci θ important subset of collisions takes place Let in a us plane. consi iar example involving φ multiple collisions collides of object with p v 2f cos φ surface. For such two-dimensional collisions, (Fig. 9.11b), we pa ob for conservation of momentum: moves at an an v2f sinφ v 2f sion. Applying m 1 1ix 1 m 2 vthat 2ix 5 the m 1 initial v 1fx 1 b m 1 v 1iy 1 m 2 v 2iy 5 m 1 v 1fy 1Dp Figure 9.11 An elastic, glancing where collision the three between subscripts two particles. on the velocity compo Dp sent, respectively, the identification of the object (1 and the velocity component (x, y). Let us consider a specific two-dimensional proble collides with particle 2 of mass m 2 initially at rest as i (Fig. 9.11b), particle 1 moves at an angle u with respec moves at an angle f with respect to the horizontal. T You would find the total initial momentum by adding the initial momentum vectors. v 1f The final momentum is found by adding the final momentum v 1f cos θ vectors. θ v 1f

23 600 N/m numerical values: served when t v 1i implies that th m important sub 1 Finalize This answer is not the maximum compression of the spring because iar example the two in m each other at the instant shown in Figure 9.10b. Can you determine 2 the surface. maximum For com su a for conservatio x m More Complicated Collisions As an example, consider the case of a glancing collision. a Before the collision v 1i m 1 m 2 After the collision v 1f sin θ φ v2f sinφ v 2f cos φ After the collision 9.5 Collisions in Two Dimension In ection 9.2, we v 1f sin showed θ that the momentum where the thr of served when the system is isolated. sent, For any respectiv collis implies that the momentum v 1f cos in θeach and of the the directi veloci θ important subset of collisions takes place Let in a us plane. consi iar example involving φ multiple collisions collides of object with p v 2f cos φ surface. For such two-dimensional collisions, (Fig. 9.11b), we pa ob for conservation of momentum: moves at an an v2f sinφ v 2f sion. Applying m 1 1ix 1 m 2 vthat 2ix 5 the m 1 initial v 1fx 1 b m 1 v 1iy 1 m 2 v 2iy 5 m 1 v 1fy 1Dp Figure 9.11 An elastic, glancing where collision the three between subscripts two particles. on the velocity compo Dp sent, respectively, the identification of the object (1 and the velocity component (x, y). Let us consider a specific two-dimensional proble collides with particle 2 of mass m 2 initially at rest as i (Fig. 9.11b), particle 1 moves at an angle u with respec moves at an angle f with respect to the horizontal. T You would find the total initial momentum by adding the initial momentum vectors. v 1f The final momentum is found by adding the final momentum v 1f cos θ vectors. θ What will p net,f be in this case? v 1f

24 Example Car collision ollisions A 1500 kg car traveling east with a speed of 25.0 m/s collides at an intersection with a 2500 kg truck traveling north at a speed of 20.0 m/s. Find the direction and magnitude of the velocity of the wreckage after the collision, assuming the vehicles stick together after the collision. ceptualize the situation before long the positive x direction and y v f ediately before and immediately, we ignore the small effect that and model the two vehicles as an ore the vehicles sizes and model tic because the car and the truck 25.0i ˆ m/s u x 20.0j ˆ m/s ng momentum in the x direction initial momentum of the system the car. imilarly, the total initial f the truck. After the collision, let espect to the x axis with speed v f. 1 erway & Jewett, page 265. Figure 9.12 (Example 9.8) An eastbound car colliding with a northbound truck.

25 Example Car collision This is an inelastic collision.

26 Example Car collision This is an inelastic collision. Initial momentum = initial momentum of car + initial momentum of truck p net,i = (1500 kg) (25.0 m/s) i + (2500 kg) (20.0 m/s) j p net,f = ( kg) v f

27 ummary sources of energy rotational motion Essay Homework due July 14th. Describe the design features of cars that make them safer for passengers in collisions. Comment on how the design of cars has changed over time to improve these features. In what other circumstances might people be involved in collisions? What is / can be done to make those collisions safer for the people involved? Make sure use physics principles (momentum, impulse) in your answers! Homework Hewitt, Ch 6, onward from page 96, Plug and chug: 1, 3, 5, 7; Ranking: 1; Exercises: 5, 7, 19, 31, 47 Ch 7, onward from page 119. Exercises: 57, 59; Probs: 7, 9