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**Unformatted text preview: **e pull F2 of spy 002 is 10.0 N
directed at 40.0 o above the horizontal. The magnitudes and directions of
these forces do not change as the save moves, and the floor and safe make
frictionless contact. Work and kinetic energy theorem: The change in kinetic
energy of an object equals the work done on the object. ∆K = K f − K i = W
Change in the kinetic
energy of a particle = Net work done on
the particle 1. = kinetic energy
before the net
work is done + During the displacement, whit is the work
done by gravitational force and the
normal force? 3. The net
work
done What is the work done by F1 and F2
during the displacement d. 2. K f = Ki + W
kinetic energy
after the net
work is done 8 r
F2 r
F1 The safe is initially stationary. What is the
speed at the end of the 8.5m displacement. The Department of Physics, CUHK The Department of Physics, CUHK
9 §6. Work done by the gravitational force
If we use mg as the gravitational
force, then the work done by the
gravitational force is: Sample problem 7-5
An initially stationary 15.0kg crate of cheese wheels is pulled via a cable, a
distance d=5.70 m up a frictionless ramp to a height of 2.5m, where it is stops. r
v 1. r
Fg = − mgd How much work is done on the crate by the
gravitational force? 2. Kf W g = mgd cos θ
W g = mgd cos 180 o 10 How much work is done by the force T from
the cable during the lift? r
d r
v0 r
Fg Ki m r
T
frictionless m The Department of Physics, CUHK h θ The Department of Physics, CUHK
11 12 2 §7. Work done by a spring force
We want to examine the work done by a
particular type of variable force – namely,
a spring force .
spring Hooke
Robert Hooke Born: 18-Jul-1635
Birthplace: Freshwater, Isle of
Wight, England
Died: 3-Mar-1703 Hooke’s law: Fx = − kx k is the spring constant The Department of Physics, CUHK The Department of Physics, CUHK
13 Work done by a spring force Work done by a spring force W s = ∑ − Fx ∆ x
In the limit as ∆ x x0
x0 Ws = Ws =
x1 x 0 x1 ∆ x
∆ W s = − Fx ∆ x 14 ∫ xf xi xf ∫x Now suppose that we displace the block along x axis while
continuing to apply a force Fa to it. The change in the kinetic
energy of the block is →0 − Fx dx ∆K = K f − K i = Wa + Ws
So if the change of kinetic energy is zero, − kxdx i W a = −W s W s = 1 kx i2 − 1 kx 2
f
2
2
If Note: Therefore, if a block is attached to a spring is stationary before and after a
displacement, the work done by the applied force displacing is the negative of the work
done on it by the spring force. xi = 0
W s = − 1 kx 2
2 The Department of Physics, CUHK The Department of Physics, CUHK
15 §8. Work done by a general variable force Sample problem 7-8
In the right figure, a cumin of mass
m=0.40kg slides across a horizontal
frictionless counter with speed
v=0.50m/s. It then runs into and
compresses a spring of spring
constant k=750N/m. When the
canister is momentarily stopped by
the spring, by what distance d is
the spring is compressed? 16 r
v k F ( x) Let’s consider a general
va...

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