Transcript Work

Physics 7C lecture 06
Work and Energy
Thursday October 17, 8:00 AM – 9:20 AM
Engineering Hall 1200
Copyright © 2012 Pearson Education Inc.
Introduction
• The simple methods we’ve learned using Newton’s
laws are inadequate when the forces are not
constant.
• In this chapter, the introduction of the new concepts
of work, energy, and the conservation of energy will
allow us to deal with such problems.
Copyright © 2012 Pearson Education Inc.
Work
• A force on a body does work if the body undergoes a
displacement.
• Figures 6.1 and 6.2 illustrate forces doing work.
Copyright © 2012 Pearson Education Inc.
Work done by a constant force
• The work done by a constant force acting at an angle  to
the displacement is W = Fs cos . Figure 6.3 illustrates this
point.
• Follow Example 6.1.
Copyright © 2012 Pearson Education Inc.
Positive, negative, and zero work
• A force can do positive, negative, or zero work depending on
the angle between the force and the displacement. Refer to
Figure 6.4.
Copyright © 2012 Pearson Education Inc.
Q6.1
An elevator is being lifted at a constant
speed by a steel cable attached to an electric
motor. Which statement is correct?
Cable
A. The cable does positive work on the
elevator, and the elevator does positive
work on the cable.
Motor
v
Elevator
B. The cable does positive work on the elevator, and the elevator
does negative work on the cable.
C. The cable does negative work on the elevator, and the
elevator does positive work on the cable.
D. The cable does negative work on the elevator, and the
elevator does negative work on the cable.
© 2012 Pearson Education, Inc.
A6.1
An elevator is being lifted at a constant
speed by a steel cable attached to an electric
motor. Which statement is correct?
Cable
A. The cable does positive work on the
elevator, and the elevator does positive
work on the cable.
Motor
v
Elevator
B. The cable does positive work on the elevator, and the elevator
does negative work on the cable.
C. The cable does negative work on the elevator, and the
elevator does positive work on the cable.
D. The cable does negative work on the elevator, and the
elevator does negative work on the cable.
© 2012 Pearson Education, Inc.
Q6.2
An elevator is being lowered at a constant
speed by a steel cable attached to an electric
motor. Which statement is correct?
Cable
A. The cable does positive work on the
elevator, and the elevator does positive
work on the cable.
Motor
v
Elevator
B. The cable does positive work on the elevator, and the elevator
does negative work on the cable.
C. The cable does negative work on the elevator, and the
elevator does positive work on the cable.
D. The cable does negative work on the elevator, and the
elevator does negative work on the cable.
© 2012 Pearson Education, Inc.
A6.2
An elevator is being lowered at a constant
speed by a steel cable attached to an electric
motor. Which statement is correct?
Cable
A. The cable does positive work on the
elevator, and the elevator does positive
work on the cable.
Motor
v
Elevator
B. The cable does positive work on the elevator, and the elevator
does negative work on the cable.
C. The cable does negative work on the elevator, and the
elevator does positive work on the cable.
D. The cable does negative work on the elevator, and the
elevator does negative work on the cable.
© 2012 Pearson Education, Inc.
Work done by several forces
• W = Wtraction + Wfriction
• or
• W = (Tx + fx ) . x
Copyright © 2012 Pearson Education Inc.
Q6.4
A tractor driving at a
constant speed pulls a
sled loaded with
firewood. There is
friction between the
sled and the road.
The total work done on the sled after it has moved a distance d is
A. positive.
B. negative.
C. zero.
D. not enough information given to decide
© 2012 Pearson Education, Inc.
A6.4
A tractor driving at a
constant speed pulls a
sled loaded with
firewood. There is
friction between the
sled and the road.
The total work done on the sled after it has moved a distance d is
A. positive.
B. negative.
C. zero.
D. not enough information given to decide
© 2012 Pearson Education, Inc.
Kinetic energy
• The kinetic energy of a particle is K = 1/2 mv2.
• The net work on a body changes its speed and therefore its kinetic
energy, as shown in Figure 6.8 below.
Copyright © 2012 Pearson Education Inc.
The work-energy theorem
• The work-energy theorem: The work done by the net
force on a particle equals the change in the particle’s
kinetic energy.
• Mathematically, the work-energy theorem is
expressed as Wtot = K2 – K1 = K.
Copyright © 2012 Pearson Education Inc.
Q6.5
A nonzero net force acts on an object. Which of the following
quantities could be constant?
A. the object’s kinetic energy
B. the object’s velocity
C. both of the above
D. none of the above
© 2012 Pearson Education, Inc.
A6.5
A nonzero net force acts on an object. Which of the following
quantities could be constant?
A. the object’s kinetic energy
B. the object’s velocity
C. both of the above
D. none of the above
© 2012 Pearson Education, Inc.
The work-energy theorem
• Wtot = K2 – K1 = K.
• Proof:
F = m dV/dt
and
dx = V dt
multiply:
F dx = m V dV = d(½ m V2) = d K
Since: d W = F dx
we have: d W = d K
or W = K2 – K1
Copyright © 2012 Pearson Education Inc.
Using work and energy to calculate speed
• with 1 N push, what is V2?
Copyright © 2012 Pearson Education Inc.
Q6.8
Three blocks are connected as
shown. The ropes and pulleys are
of negligible mass. When released,
block C moves downward, block B
moves up the ramp, and block A
moves to the right.
After each block has moved a distance d, the force of gravity has done
A. positive work on A, B, and C.
B. zero work on A, positive work on B, and negative work on C.
C. zero work on A, negative work on B, and positive work on C.
D. none of these
© 2012 Pearson Education, Inc.
A6.8
Three blocks are connected as
shown. The ropes and pulleys are
of negligible mass. When released,
block C moves downward, block B
moves up the ramp, and block A
moves to the right.
After each block has moved a distance d, the force of gravity has done
A. positive work on A, B, and C.
B. zero work on A, positive work on B, and negative work on C.
C. zero work on A, negative work on B, and positive work on C.
D. none of these
© 2012 Pearson Education, Inc.
Work and energy with varying forces—Figure 6.16
• Many forces, such as the
force to stretch a spring,
are not constant.
• In Figure 6.16, we
approximate the work by
dividing the total
displacement into many
small segments.
Copyright © 2012 Pearson Education Inc.
Stretching a spring
• The force required to stretch a
spring a distance x is
proportional to x: Fx = kx.
• k is the force constant (or
spring constant) of the spring.
• The area under the graph
represents the work done on
the spring to stretch it a
distance X: W = 1/2 kX2.
Copyright © 2012 Pearson Education Inc.
Motion with a varying force
• An air-track glider is attached to a spring, so the force on
the glider is varying.
• For initial speed v1, how long can the spring extend?
Copyright © 2012 Pearson Education Inc.
Motion with a varying force
• For initial speed v1, how long can the spring extend?
½ m v12 = ½ k x2
Copyright © 2012 Pearson Education Inc.
Motion with a varying force
• For initial speed v1, how long can the spring extend?
½ m v12 = ½ k x2 + fk x
Copyright © 2012 Pearson Education Inc.
Motion on a curved path—Example 6.8
• A child on a swing moves along a curved path.
• write down all the work(s)
Copyright © 2012 Pearson Education Inc.
Motion on a curved path—Example 6.8
• gravity: mg R (1-cos θ)
• push: F R sin θ
• tension in the string: 0
Copyright © 2012 Pearson Education Inc.
(Why?)
Q6.6
A 6.00-kg block and an 8.00-kg block
are connected as shown. When released,
the 6.00-kg block accelerates downward
and the 8.00-kg block accelerates to the
right. After each block has moved 2.00
cm, the force of gravity has done
A. more work on the 8.00-kg block than on the 6.00-kg block.
B. the same amount of work on both blocks.
C. less work on the 8.00-kg block than on the 6.00-kg block.
D. not enough information given to decide
© 2012 Pearson Education, Inc.
A6.6
A 6.00-kg block and an 8.00-kg block
are connected as shown. When released,
the 6.00-kg block accelerates downward
and the 8.00-kg block accelerates to the
right. After each block has moved 2.00
cm, the force of gravity has done
A. more work on the 8.00-kg block than on the 6.00-kg block.
B. the same amount of work on both blocks.
C. less work on the 8.00-kg block than on the 6.00-kg block.
D. not enough information given to decide
© 2012 Pearson Education, Inc.
Q6.7
A 6.00-kg block and an 8.00-kg block
are connected as shown. When released,
the 6.00-kg block accelerates downward
and the 8.00-kg block accelerates to the
right. After each block has moved 2.00
cm, the total work done on the 8.00-kg
block
A. is greater than the total work done on the 6.00-kg block.
B. is the same as the total work done on the 6.00-kg block.
C. is less than the total work done on the 6.00-kg block.
D. not enough information given to decide
© 2012 Pearson Education, Inc.
A6.7
A 6.00-kg block and an 8.00-kg block
are connected as shown. When released,
the 6.00-kg block accelerates downward
and the 8.00-kg block accelerates to the
right. After each block has moved 2.00
cm, the total work done on the 8.00-kg
block
A. is greater than the total work done on the 6.00-kg block.
B. is the same as the total work done on the 6.00-kg block.
C. is less than the total work done on the 6.00-kg block.
D. not enough information given to decide
© 2012 Pearson Education, Inc.
Power
• Power is the rate at which work
is done.
• Average power is Pav = W/t
and instantaneous power is P =
dW/dt.
• The SI unit of power is the watt
(1 W = 1 J/s), but other familiar
units are the horsepower and the
kilowatt-hour.
Copyright © 2012 Pearson Education Inc.
Q6.10
An object is initially at rest. A net force (which always
points in the same direction) is applied to the object so
that the power of the net force is constant. As the
object gains speed,
A. the magnitude of the net force remains constant.
B. the magnitude of the net force increases.
C. the magnitude of the net force decreases.
D. not enough information given to decide
© 2012 Pearson Education, Inc.
A6.10
An object is initially at rest. A net force (which always
points in the same direction) is applied to the object so
that the power of the net force is constant. As the
object gains speed,
A. the magnitude of the net force remains constant.
B. the magnitude of the net force increases.
C. the magnitude of the net force decreases.
D. not enough information given to decide
© 2012 Pearson Education, Inc.
Summary
• Calculate the work done by a force
• Kinetic energy: Ek = ½ m v2
• work - energy theorem
• To relate work and kinetic energy when the
forces are not constant or the body follows a
curved path
• power P = dW/dt
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.