




























Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Following points are the summary of these Lecture Slides : Work Done by Varying Forces, Variable Force, Object, acting, Displacement, Versus, Variable Force, Energy Stored, Potential, Spring Constant
Typology: Slides
1 / 36
This page cannot be seen from the preview
Don't miss anything!
5
x (m)
Fx (N)
F 3
F 2
F 1
x 1 x 2 x 3
The work done by F 1 is ( 0 ) 1 1 1
W = F x −
Example: What is the work done by the variable force shown below?
The net work is then W 1 +W 2 +W3.
The work done by F 2 is ( ) 2 2 2 1
W = F x − x
The work done by F 3 is (^) ( ) 3 3 3 2
7
Example: (a) If forces of 5.0 N applied to each end of a spring cause the spring
to stretch 3.5 cm from its relaxed length, how far does a force of 7.0 N cause the
same spring to stretch? (b) What is the spring constant of this spring?
2
1
2
1
Solving for x 2 : (^) ( 3. 5 cm) 4. 9 cm.
5.0 N
1
1
2 2 ⎟ =
⎠
⎞ ⎜
⎝
⎛ = x =
F
F x
3.5 cm
1
1 = = =
x
k
(b) What is the spring constant of this spring? Use Hooke’s law:
4.9 cm
2
2 = = =
x
Or k
8
Example: An ideal spring has k = 20.0 N/m. What is the amount of work done
(by an external agent) to stretch the spring 0.40 m from its relaxed length?
Fx (N)
x (m) x 1 =0.4 m
kx 1
( )( ) ( 20. 0 N/m)( 0. 4 m) 1. 6 J
2
1
2
1
2
1
Area under curve
2 2 1 1 1 = = = =
=
kx x kx
W
Conservation of Energy including a Spring
the conservation of energy equation
g s i g s f
( KE + PE + PE ) = ( KE + PE + PE )
11
Example: A box of mass 0.25 kg slides along a horizontal, frictionless surface
with a speed of 3.0 m/s. The box encounters a spring with k = 200 N/m. How
far is the spring compressed when the box is brought to rest?
2 2
v
k
m x
mv kx
i i f f
i f
Given:
m = 0.25 kg
k = 200 N/m
vi = 3.0 m/s
vf = 0 m/s
Find:
x =?
Idea: we are given velocity, mass and spring constant.
Let’s use conservation of energy: kinetic energy pf the
box was transformed into elastic potential energy of the
spring.
nc f f i i
nc f i i f
of the system
through a medium
water, seismic
electrical current
Problem Solving with Nonconservative
Forces
initial total energy
Energy problems
2
2
s
kg m
s
J W
= =
22
Example: A race car with a mass of 500.0 kg completes a quarter-mile (402 m)
race in a time of 4.2 s starting from rest. The car’s final speed is 125 m/s.
What is the engine’s average power output? Neglect friction and air resistance.
5
2
av
t
mv
t
t
t
f
Given:
m=500.0 kg
s = 402 m
t = 4.2 s
vf = 125 m/s
vi = 0 m/s
Find:
P =?
Idea: to compute power we need energy and time. Time
is given, while energy (kinetic) can be computed
Notice that the distance information was not needed.
considered to be concentrated
related to the change in height of the center of mass