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Work, Energy, and Power - Lesson 1 - Basic Terminology a n d
Concepts
Definition and Mathematics of Work
http://www.phvsicsclassroom.com/class/energv/Lesson-l/Definition-and-Mathematics-of-Work
1. When is work d o n e on an object?
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C i b i t c - f
2. What are the 3 key ingredients to work?
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- C c v u > c
3. What are 2 everyday examples of work?
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4
4. Quiz: Read the 4 statements on the p a g e a n d answer whether or not work
has been done.
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) Hb
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b)
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) Ho —•>
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5. What is the work equation?
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0 rv V ^
p ' f'Ci ( C'-f
d d r 5 | ) ( c ( € ^ e ^
-6. What angle is used?
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d
d f ^ p l C > C ^ W 7
r \ J t X . . f o rJ 1
7. Explain scenario A, B, a n d C for angles used in the work equation.
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a8. Why does a vertical force never d o work on a horizontally displaced
object?
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-9. Why d o you need to b e careful doing calculations up ramps, w h e n the
force a n d the displacement are in the exact same direction?
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10.Go to the animation. How is it possible that the least steep mountain a n d
the steepest mountain require the same amount of work (and gasoline)?
Explain in detail!
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11. What is negative work?
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12. What is the unit of work? What is it equivalent to?
13. Do the investigate a t the bottom of the page. Put in your information.
Write d o w n your information below. Calculate how much work it would
take you to d o the given exercise. Write down work, as well as calories/fat
burned.
various oAStoers
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c u t s L A X x y h t , h e t g h f c , ^
.
14.Complete the attached it's an Uphill Interactive.
Go t o the next section!
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15.Complete the 3 calculations for the c h e c k your understanding question
o n e below.
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. . X - « . V . - A / 2A , W / >t x j f l ) n / .
N - ( i c o ) ( s ) ( o s 3 0
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16.See question two. Draw each of the free b o d y diagrams. List what f o r c e is
doing the work. Complete the equation to get an answer of h o w m u c h
work is being done.
a ) A 1 0 - N f o r c e i s a p p l i e d t o p u s h a b l o c k a c r o s s a f r i c t i o n f r e e s u r f a c e f o r a d i s p l a c e m e n t o f
5 0 m
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, h e r i g h t'
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F
0 l Mf i r e .
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b ) A 1 0 - N f r i c t i o n a l f o r c e s l o w s a m o v i n g b l o c k t o a s t o p a f t e r a d i s p l a c e m e n t o f 5 . 0 m t o t h e
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-
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4 /
Jc ) A 1 0 - N f o r c e i s a p p l i e d t o p u s h a b l o c k a c r o s s a f r i c t i o n a l s u r f a c e a t c o n s t a n t s p e e d f o r a d i s p l a c e m e n t o f 5 . 0 m t o t h e r i g h t .
\
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w „ 1 1 06 T f v * " V X — V — .
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r c.
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/
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d ) A n a p p r o x i m a t e l y 2 - k g o b j e c t i s s l i d i n g a t c o n s t a n t s p e e d a c r o s s a friction fr e e s u r f a c e f o r a
d i s p l a c e m e n t o f 5 m t o t h e r i g h t .
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e ) A n ap p r o x i m a t e l y 2 - k g o b j e c t i s p u l l e d u p w a r d a t c o n s t a n t s p e e d b y a 2 0 - N f o r c e f o r a v e r t i c a l d i s p l a c e m e n t o f 5 m .
9 ( ) r V d t> w W k
7.
B e f o r e b e g i n n i n g i t s i n i t i a l d e s c e n t , a r o l l e r c o a s t e r c a r i s a l w a y s p u l l e d u p t h e f i r s t h i l l t o a h i g hi n i t i a l h e i g h t . W o r k is d o n e o n t h e c a r ( u s u a l l y b y a c h a i n ) t o a c h i e v e t h i s i n i t i a l h e i g h t . A c o a s t e r d e s i g n e r i s c o n s i d e r i n g t h r e e d i f f e r e n t i n c l i n e a n g l e s a t w h i c h t o d r a g t h e 2 0 0 0 - k g c a r t r a i n t o t h e t o p o f th e 6 0 - m e t e r h i g h h i l l . I n e a c h c a s e , t h e f o r c e a p p l i e d t o t h e c a r w i l l b e a p p l i e d p a r a l l e l t o t h e h i l l . H e r c r i t i c a l q u e s t i o n i s : w h i c h a n g l e w o u l d r e q u i r e t h e m o s t w o r k ? A n a l y z e t h e d a t a , d e t e r m i n e t h e w o r k d o n e i n e a c h c a s e , a n d a n s w e r t h i s c r i t i c a l q u e s t i o n .
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1 8 . B e n T r a v l u n c a r r i e s a 2 0 0 - N s u i t c a s e u p t h r e e f l i g h t s o f st a i r s ( a h e i g h t o f 1 0 . 0 m ) a n d t h e n p u s h e s i t w i t h a h o r i z o n t a l f o r c e o f 5 0 . 0 N a t a c o n s t a n t s p e e d o f 0 . 5 m / s f o r a h o r i z o n t a l d i s t a n c e o f 3 5 . 0 m e t e r s . H o w m u c h w o r k d o e s B e n d o o n h i s s u i t c a s e d u r i n g t h i s e n t i r e m o t i o n ?
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1 9 . A f o r c e o f 5 0 N a c t s o n t h e b l o c k a t t h e a n g l e s h o w n i n t h e d i a g r a m . T h e b l o c k m o v e s a h o r i z o n t a l d i s t a n c e o f 3 . 0 m . H o w m u c h w o r k i s d o n e b y t h e a p p l i e d f o r c e ?
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w ' i tk A. ^ "X
2 0 . How much work is done by an applied force to lift a 15-Newton block 3 . 0 meters vertically at a constant speed?
21 . A s t u d e n t w i t h a m a s s o f 8 0 . 0 k g r u n s u p t h r e e f l i g h t s o f st a i r s i n 1 2 . 0 s e c . T h e s t u d e n t h a s g o n e a
v e r t i c a l d i s t a n c e o f 8 . 0 m . D e t e r m i n e t h e a m o u n t o f w o r k d o n e b y t h e s t u d e n t t o e l e v a t e h i s b o d y t o t h i s h e i g h t . A s s u m e t h a t h i s s p e e d i s c o n s t a n t .
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( = 2 7 5 -
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2 2 . C a l c u l a t e t h e w o r k d o n e b y a 2 . 0 - N f o r c e ( d i r e c t e d a t a 3 0 ° a n g l e t o t h e v e r t i c a l ) t o m o v e a 5 0 g r a m b o x a h o r i z o n t a l d i s t a n c e o f 4 0 0 c m a c r o s s a r o u g h f l o o r a t a c o n s t a n t s p e e d o f 0 . 5 m / s . ( H I N T : B e c a u t i o u s w i t h t h e u n i t s . ) v ~ 4 / z . )
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v ~
f d ( . o s bV
U >2 3 . A t i r e d s q u i r r e l ( m a s s o f 1 k g ) d o e s p u s h - u p s b y a p p l y i n g a f o r c e t o e l e v a t e i t s c e n t e r - o f - m a s s b y 5 c m . E s t i m a t e t h e n u m b e r o f pu s h - u p s t h a t a t i r e d s q u i r r e l m u s t d o i n o r d e r t o d o a
a p p r o x i m a t e l y 5 . 0 J o u l e s o f w o r k .
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Cos 0
w -
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I O p u S h ' V p S
From The Physics Classroom's Physics Interactive http://www.physicsclassroom.com
It's All Uphill Interactive
Background:
I n t h i s I n t e r a c t i v e , y o u w i l l a n a l y z e t h e m o t i o n o f a c a r t b e i n g p u l l e d u p a n i n c l i n e d p l a n e a t a c o n s t a n t s p e e d . T h e a n g l e o f th e i n c l i n e c a n b e m o d i f i e d b y 1 0 ° i n c r e m e n t s b e t w e e n t h e v a l u e s o f 3 0 ° a n d 9 0 ° . T h r e e d i f f e r e n t m a s s e s c a n b e s e l e c t e d - 2 . 0 k g , 3 . 0 k g , a n d 4 . 0 k g . I n e a c h s i m u l a t i o n , t h e c a r t i s p u l l e d t o t h e s a m e h e i g h t - 1 . 0 m e t e r a b o v e t h e o r i g i n a l s t a r t i n g p o s i t i o n . F o r e a c h s i m u l a t i o n , t h e f o r c e t h a t m u s t b e a p p l i e d i s r e p o r t e d o n t h e s c r e e n . T h e d i s p l a c e m e n t o f th e c a r t c a n b e m e a s u r e d u s i n g t h e c m - r u l e r t h a t i s d i s p l a y e d f o r e a c h t r i a l .
Purpose:
T o d e t e r m i n e t h e e f f e c t o f th e a n g l e o f a n i n c l i n e d p l a n e u p o n t h e a m o u n t o f fo r c e a n d t h e a m o u n t o f w o r k d o n e w h e n p u l l i n g a c a r t u p a n i n c l i n e d p l a n e a t a c o n s t a n t s p e e d a n d t o t h e s a m e h e i g h t .
Discussion of Procedure:
S e l e c t a m a s s f r o m o n e o f th e t h r e e c h o i c e s . T a p t h e Run Trial b u t t o n . T h e f o r c e r e q u i r e d t o p u l l t h e c a r t a t a c o n s t a n t s p e e d i s d i s p l a y e d o n t h e s c r e e n ; r e c o r d i n t h e D a t a T a b l e . T h e d i s p l a c e m e n t f r o m t h e s t a r t i n g p o s i t i o n t o t h e f i n a l p o s i t i o n c a n b e m e a s u r e d u s i n g t h e c m -r u l e -r ; -r e c o -r d i n t h e D a t a T a b l e . ( N o t e t h a t t h e t a b l e l i s t s m e t e -r s a s t h e u n i t . ) T h e f o -r c e a n d t h e d i s p l a c e m e n t v e c t o r s a r e b o t h d i r e c t e d p a r a l l e l t o t h e i n c l i n e d p l a n e . U s e t h e f o r c e a n d d i s p l a c e m e n t t o c a l c u l a t e t h e w o r k d o n e . R e p e a t t h e p r o c e d u r e f o r a l l a n g l e s .
D a t a t a b l e s a r e p r o v i d e d f o r a s i n g l e c a r t m a s s . A d d i t i o n a l t a b l e s c a n b e m a d e i f n e c e s s a r y .
Data: ky Cc">Q
M a s s : ° k g
Angle (°) Force (N) Displacement (m) Work (J)
30.0 | 4 , 1
X
a s
40.0
\ I A
I i6T 2 9-50.0 l , a ^ I S
60.0 a s - s . h i M
70.0 3 1 , b
!
80.0
\
5
90.0 a M 0 , ^
o
^ r e s u l t s vUill v c u i , ckpenoLuao o n m a s s o.?ed
b x i W J W c a t uuuLi h a v € t h e
b %r•
See b a d e - f i y tr-endr
F r o m The Physics Classroom's Physics Interactive http://www.physicsclassroom.com
Analysis:
1 . I n t h e s p a c e b e l o w , c o n s t r u c t p l o t s o f fo r c e a n d w o r k a s a f u n c t i o n o f th e i n c l i n e a n g l e . L a b e l t h e d i v i s i o n s a l o n g t h e a x e s . C o n s t r u c t t h e b e s t - f i t l i n e t h r o u g h t h e d a t a .
2.
z
<
D
O
o
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<0
5
• ? <
TO
O r>
fO
70
A n g l e ( ° )
' V V V *
0 A n g l e ( ° )D e s c r i b e h o w v a r y i n g t h e i n c l i n e a n g l e a f f e c t s t h e f o r c e ( i f a t a l l ) .
I k e S)eep€Z
+ h t .A c l ? W
/S t e
ft / j f & t s3 . D e s c r i b e h o w v a r y i n g t h e i n c l i n e a n g l e a f f e c t s t h e w o r k ( i f a t a l l ) .
^ v t f p - e r - A l t f V i c h h t / M
|i?ss
-"$• © W &
W h e n w o r k i s d o n e b y a n a p p l i e d f o r c e , t h e o b j e c t ' s e n e r g y w i l l c h a n g e . I n t h i s I n t e r a c t i v e , d o e s t h e w o r k c a u s e a k i n e t i c e n e r g y c h a n g e o r a p o t e n t i a l e n e r g y c h a n g e ?
E x p l a i n y o u r l o g i c .
A s s u m i n g t h e s t a r t i n g h e i g h t i s 0 . 0 m , c a l c u l a t e t h e p o t e n t i a l e n e r g y o f th e c a r t a f t e r i t h a s
" b e e n e l e v a t e d t o a h e i g h t o f l . 0 m a b o v e t h e s t a r t i n g l o c a t i o n . Please Show Your Work.
H o w d o e s y o u r a n s w e r t o q u e s t i o n # 5 c o m p a r e t o t h e w o r k v a l u e s i n t h e d a t a t a b l e ?
Conclusion:
S t a t e a t w o - p a r t c o n c l u s i o n i n w h i c h y o u d e s c r i b e t h e e f f e c t o f th e i n c l i n e d a n g l e u p o n t h e . . . • a m o u n t o f fo r c e r e q u i r e d t o p u l l t h e c a r t u p t h e h i l l a t a c o n s t a n t s p e e d .
• a m o u n t o f w o r k d o n e w h e n p u l l i n g t h e c a r t u p t h e h i l l a t a c o n s t a n t s p e e d .
