Transcript L14_KE - barransclass

Kinetic Energy
work of changing speed
§ 6.2
Rebounding Ball
What is the sign of the work done on the ball
by the wall as it slows (squishes)?
A.
B.
C.
D.
Positive (W > 0).
Negative (W < 0).
Zero (W = 0).
Can’t tell (W = ?).
Rebounding Ball
What is the sign of the work done on the ball
by the wall as it rebounds (expands)?
A.
B.
C.
D.
Positive (W > 0).
Negative (W < 0).
Zero (W = 0).
Can’t tell (W = ?).
Happy/Sad Balls
Which ball has the greatest change in kinetic
energy DK during impact?
A. The happy (rebounding) ball.
B. The sad (dead) ball.
C. Both had the same DK.
Happy/Sad Balls
Which ball has the most (largest absolute
value) work done on it during impact?
A. The happy (rebounding) ball.
B. The sad (dead) ball.
C. Both had the same W.
Work in General
changing forces, curving paths
§ 6.3
What’s the point?
• What is work when force is not constant or
the path is not straight?
Work in General
• For constant force, W = F·s.
• F may vary with position or time.
• Path may not be straight.
• In general, dW = F·ds.
• So, W = F·ds.
• (Sum of work done over each interval.)
Elastic Force
Stretching and squishing
still § 6.3
Hooke’s Law Formula
F = –kx
F = force exerted by the spring
k = spring constant; units: N/m; k > 0
x = displacement from equilibrium position
negative sign: force opposes distortion
Work to Deform a Spring
• Push or pull a distance x from equilibrium
slope = k
kx
area = w
force
displacement
• Work =
1
2
• Work =
1
2 kx·x
F·x ; F = kx
1
=
2
kx2
x
Poll Question
A spring with force constant k is stretched
from x = 0 to x = D. What is the work done
by the spring as it stretches?
A.
B.
C.
D.
E.
1/2 kD2.
–1/2 kD2.
0.
It cannot be determined.
None of these.
Poll Question
Two springs, one with a spring constant k1 and the other
with a spring constant k2 = 2 k1, are slowly stretched to the
same final tension. Which spring has more work done on
it?
A. The stiffer spring (k = k2 = 2 k1)
B. The softer spring (k = k1)
C. The same work was done on both.
Centripetal Force
work of acceleration
§ 6.3
Group Poll Question
A toy of mass m moving at constant speed v in a
circle of radius r has a constant magnitude of
centripetal acceleration of v2/r. Its velocity
reverses every half-cycle.
How much work does the centripetal force do on
the toy every half-cycle?
A.
B.
C.
D.
mv2.
–mv2.
pmv2.
None of these.
Kinetic Energy and Direction
• K depends on speed
• Direction of velocity is irrelevant
• Changing only direction requires force, but
no work.
• 1/2 mv2 = 1/2 mvv is a scalar.
Net Force and Net Work
• Net force is nonzero if a body accelerates
• net work is nonzero if a body changes
speed
• The net force must overlap with the
displacement to do work!