Introduction to Mechanics Energy Conservation Examples

Transcription

1 Introduction to Mechanics Energy Conservation Examples Lana heridan De Anza College Nov 30, 2017

2 Last time energy conservation

3 Overview more practice with energy conservation

4 How to olve Energy Conservation Problems 1 Draw (a) diagram(s). Free body diagrams or full pictures, as needed. 2 Make a hypothesis or estimate of what the answer will be. 3 Identify the system. tate what it is. Is it isolated? 4 Identify the initial point / configuration of the system. 5 Identify the final point / configuration of the system. 6 Write the energy conservation equation. 7 Fill in the expressions as needed. 8 olve. 9 Analyze answer: reasonable value?, check units, etc.

5 Energy Conservation: Example 8-10 ENERGY A block of mass m 1 = 2.40 kg is connected to a second block of mass m 2 = 1.80 kg. When the blocks are released from rest, they move through a distance d = m, at which point m 2 hits the floor. mgiven 2 = 1.80 that kg, as the shown coefficient here. When of kinetic the blocks friction are released between m 1 and the horizontal m 2 hits the surface floor. Given is µ k that = the 0.450, coefficient find the of kinetic speedfric- of the blocks just before m 2 lands. m 2 lands. lock of mass t which point 0, find the speed of the blocks just before ravitapotens; it is e of h. h i and m 1 i d f y h in this lculate e nonrms of There- i f m 2 d 0

6 hud Example 8-10 ted to a second block of mass m 2 = 1.80 kg, as shown here. When the blocks are released e d = m, at which point m 2 hits the floor. Given that the coefficient of kinetic fricface is m k = 0.450, find the speed of the blocks just before m 2 lands. therefore, the gravitaen it lands. The potenring this process; it is o know the value of h. nding points with i and m 1 i d f y h ) is doing work in this hus, we must calculate d E f, but also the nonn be written in terms of before m 2 lands. Therelve for the final speed. clude contributions hat E f depends, W nc. Recall that the g, and that it points E i = U i + K i = m 1 gh + m 2 gd W nc = -f k d = -m k m 1 gd m 2 i d f 0 ystem: Masses m 1 and m 2, modeled as point particles, and the Earth. U i = m 1 gh K i = 1 2 m # + m 2 gd W 1 2 m # 2 0 ext 2 = 0= K + U Here: U f = m 1 gh + 0 W ext = W nc = f k d K f = 1 2 m 1v m 2v K is the change 2 E f = U f in K.E. + K f = m 1 of both masses gh m 1v m 2v 2 U is the change in Grav. P.E. of the masses (only m 2 s changes)

7 Example 8-10 Points i and f are as labelled in the diagram. W ext = K + U W ext = (K 1,f + K 2,f 0 K 1,i 0 K 2,i ) + ( 0 U f U i ) f k d = ( 1 2 (m 1 + m 2 )v 2 0) + (0 m 2 gd) v = 2(m 2 µ k m 1 )gd m 1 + m 2 = 1.30 m/s

8 Example: Box liding Down an Incline A 3.00 kg crate slides down a ramp. The ramp is 1.00 m in length and inclined at an angle of The crate starts from rest at the top, experiences a constant friction force of magnitude 5.00 N, and continues to move a short distance on the horizontal floor after it AMleaves the ramp. 0 m in length and he crate starts from f magnitude 5.00 N, zontal floor after it v i m 0 d 1.00 m 30.0 v f e crate at the bot- Use energy methods Figure to8.10 determine (Example the 8.7) A speed crate slides of the crate at the amp in Figure down a ramp under the influence of gravity. will slide. bottom of the ramp. The potential energy of the system decreases, whereas the kinetic energy increases. Earth as an isolated

9 Imagine the crate sliding down the ramp in Figure friction force, the more slowly the crate will slide. Figure 8.10 (Example 8.7) A crate slides down a ramp under the influence of gravity. The potential energy of the system decreases, Example: Box liding Down an Incline A 3.00 kg crate slides down a ramp. The ramp is 1.00 m in length and inclined at an angle of The crate starts from rest at the top, experiences a constant friction force of magnitude 5.00 N, and continues to move a short distance on the horizontal floor after it leaves the ramp. Chapter 8 Conservation of Energy Crate liding Down a Ramp AM ystem: crate + Earth. e slides down a ramp. The ramp is 1.00 m in length and angle i : of crate as shown at top in Figure of ramp The crate starts from experiences a constant friction force of magnitude 5.00 N, to move a short distance on the horizontal floor after it p. f : crate at bottom of ramp, choose y = 0, U = 0 at this point y methods to determine the speed of the crate at the botp. ystem is nonisolated. v i m 0 d 1.00 m 30.0 v f

10 Example: Box liding Down an Incline Let the ground level represent the zero of gravitational potential. K + U = W fric

11 Example: Box liding Down an Incline Let the ground level represent the zero of gravitational potential. K + U = W fric 0 (K f K i ) + ( U 0 f U i ) = f k d 1 2 mv 2 mgh = f k d 1 2 mv 2 mgd sin θ = f k d 2(mgd sin θ fk d) v = m 2(14.7 5) = ms 1 3 = 2.54 ms 1

12 Example, Part 2: liding Off Ramp A 3.00 kg crate slides down a ramp. The ramp is 1.00 m in length and inclined at an angle of The crate starts from rest at the top, experiences a constant friction force of magnitude 5.00 N, and continues to move a short distance on the horizontal floor after it AMleaves the ramp. 0 m in length and he crate starts from f magnitude 5.00 N, zontal floor after it v i m 0 d 1.00 m 30.0 v f e crate at the bot- How far does the Figure crate8.10 slide (Example on the8.7) horizontal A crate slides floor if it continues amp in Figure down a ramp under the influence of gravity. will slide. to experience a The friction potential force energy of magnitude of the system decreases, 5.00 N? whereas the kinetic energy increases. Earth as an isolated

13 Example, Part 2: liding Off Ramp How far does the crate slide on the horizontal floor if it continues AMto experience a friction force of magnitude 5.00 N? 0 m in length and he crate starts from f magnitude 5.00 N, zontal floor after it v i m 0 d 1.00 m 30.0 v f e crate at the bot- ystem: crate. Figure 8.10 (Example 8.7) A crate slides amp in Figure down a ramp under the influence of gravity. will slide. The potential energy of the system decreases, i : crate at bottom whereas ofthe ramp kinetic energy increases. Earth as an isolated f : crate distance s from bottom of ramp, at rest e system ystem when the is nonisolated. crate the top of the ramp is zero. If the y (the final position of the crate, for which we choose the gravita-

14 Example, Part 2: liding Off Ramp How far does the crate slide on the horizontal floor if it continues to experience a friction force of magnitude 5.00 N? K = W fric mv 2 i = f k s s = 1 mvi 2 2f k s = 1 2(5 N) (3 kg)(2.54 ms 1 ) 2 s = 1.94 m

15 ummary energy conservation practice Homework Review: Relative motion worksheet (due Tuesday, Dec 5)