Energy Unit: Physics 11 Work & Gravitational Potential Energy Mechanical work: Equation: a measure of the amount of energy transferred when a force acts over a given displacement. units: ( also (Neuha-nfrQ) The Conditions for Mechanical Work 1. A force must be exerted on an object. 2. The object must be displaced by the force. 3. At least part of the force must be in the same direction as the displacement or the exact opposite direction. Positive work The force and displacement are in the same direction, which adds energy tothe system. Negative work The force and displacement are in opposite directions, which removes energy from the system. w = Fd cos(00) Maximum energy added i; W Fd cos(900) Zero energy added W = Fd cos(1800) Maximum energy subtracted Model: A girl pulls her brother along in a trolley for a distance of 30 m, as shown. Calculate the work done on the trolley. 50 N Direction Of motion e— Vlog. 

Scene 1

Energy Unit: Physics 11
Work & Gravitational Potential Energy
Mechanical work:
Equation:
a measure of the amount of energy transferred when a force acts over a given displacement.
units: (
also (Neuha-nfrQ)
The Conditions for Mechanical Work
1. A force must be exerted on an object.
2. The object must be displaced by the force.
3. At least part of the force must be in the same direction as the displacement or the exact opposite direction.
Positive work The force and displacement are in the same direction, which adds energy tothe system.
Negative work The force and displacement are in opposite directions, which removes energy from the system.
w = Fd cos(00)
Maximum energy added
i;
W Fd cos(900)
Zero energy added
W = Fd cos(1800)
Maximum energy subtracted
Model:
A girl pulls her brother along in a trolley for a distance of 30 m, as shown. Calculate the work done
on the trolley.
50 N
Direction Of motion
e— Vlog

Model: Positive and Negative Work A shopper pushes a shoppingcart on a horizontal surface with a horizontal applied force of 41.0 N for 11.0 m. The cart experiences a force of friction of 35.0 N. Calculate the total mechanical work done on the shopping cart. a. Calculate the work done bythe applied force. b. Calculate the work done bythe force of friction. c. Calculate the total or net work done on the cart. We Graphing Work Done (s area cwrJC oe fora vs posiiiVé f work F d 0 work c) Two 91S-35S)Cllm) WA R > WA — VVR C B6CS w Q-- (OCT d Stretch displacement film Idownl) Gravitational Potential Energy Potential energy is the energy an object possesses because of its position in relation to forces in its environment. Gravitational Potential Energy refers to the energy possessed by an object due to its position relative to the surface of Earth. To develop an expression for GPE, consider the work done lifting an object at a constant speed: Units Analysis: = Reference point CROSC vvkeæ D Model V Z A roller coaster with a mass of 220 kg poised at point A Calculate: a) the gravitational energy at A with reference to the ground b) the change in gravitational energy going from B to C Is it scalar o vector? IOS* 30 m 20 m -20m) m.ur16 was bsk. 

Scene 2

Model: Positive and Negative Work
A shopper pushes a shoppingcart on a horizontal surface with a horizontal applied force of 41.0 N for 11.0 m. The cart
experiences a force of friction of 35.0 N. Calculate the total mechanical work done on the shopping cart.
a. Calculate the work done bythe applied force.
b. Calculate the work done bythe force of friction.
c. Calculate the total or net work done on the cart.
We
Graphing Work Done
(s area
cwrJC
oe fora vs
posiiiVé f
work F
d
0
work
c) Two
91S-35S)Cllm)
WA R > WA — VVR
C B6CS
w Q-- (OCT
d
Stretch displacement film Idownl)
Gravitational Potential Energy
Potential energy is the energy an object possesses because of its position in relation to forces in its environment. Gravitational
Potential Energy refers to the energy possessed by an object due to its position relative to the surface of Earth.
To develop an expression for GPE, consider the work done lifting an object at a constant speed:
Units Analysis: =
Reference point
CROSC vvkeæ D
Model V Z
A roller coaster with a mass of 220 kg poised at point A Calculate:
a) the gravitational energy at A with reference to the ground
b) the change in gravitational energy going from B to C
Is it scalar o vector?
IOS*
30 m
20 m
-20m)
m.ur16 was bsk

Work - Homework 2. A 25.0 N applied force acts on a cart in the direction of the motion. The cart moves 13.0 m. How much work is done by the applied force? (325 J) A child pulls a wagon by the handle along a flat sidewalk. She exerts a force of 80.0 N at an angle of 30.00 above the horizontal while she moves the wagon 12 m forward. The force ot friction on the wagon is 34 N. a. Calculate the mechanical work done by the child on the wagon. {830 J) b. Calculate the total work done on the wagon. (420 J) = AL3.q T 3. A 62 kgperson in an elevator is moving up ata constant speed Of 4.0m/s for 5.0 s. a. Draw an FBD of the person in the elevator. b. Calculate the work done by the normal torce on the person. c. Calculate the work done by the force of gravity on the person. (1.2 * 103 J) d. How would your answ•ers change if the elevator were moving down at 4.0 m/s for 5.0 s? (—1.2 103 J) 9 4. = Cfi ape 06 ; 40 A rope pulls a 2.0 kg bucket straight up, accelerating it from rest at 2.2 m/s2 for 3.0 s. a. Calculate. the displacement of the bucket. (9.9 m) = -190 J, F.*-240J) b. Calculate the work done by each force acting on the bucket. (F, c. Calculate the total mechanical work done on the bucket. (44 J) d. Calculate the net force acting on the bucket and the work done by the net force. Compare your answer to the total mechanical work done on the bucket as calculated in (C). (4.4 N) 5. The graph in Figure 11 shows the force acting on a cart from a spring. The force from the spring is either in the same irection as the cart's displacement or in the opposite direction. a. Calculate the work done in sections A, B, and C. (10 J, 2.5 J, -2.5 J) b. Calculate the total work done. (10 J) c. Explain why the work done in section C must be negative. -B 3 Z.SJ -2ST C 2.CS 10 > -uSS c) -m pos. 

Scene 3

Work - Homework
2.
A 25.0 N applied force acts on a cart in the direction of the motion. The cart moves 13.0 m. How much work is done by the applied
force? (325 J)
A child pulls a wagon by the handle along a flat sidewalk. She exerts a force of 80.0 N at an angle of 30.00 above the horizontal while she
moves the wagon 12 m forward. The force ot friction on the wagon is 34 N.
a. Calculate the mechanical work done by the child on the wagon. {830 J)
b. Calculate the total work done on the wagon. (420 J)
= AL3.q T
3. A 62 kgperson in an elevator is moving up ata constant speed Of 4.0m/s for 5.0 s.
a. Draw an FBD of the person in the elevator.
b. Calculate the work done by the normal torce on the person.
c. Calculate the work done by the force of gravity on the person. (1.2 * 103 J)
d. How would your answ•ers change if the elevator were moving down at 4.0 m/s for 5.0 s? (—1.2 103 J)
9
4.
= Cfi
ape 06 ; 40
A rope pulls a 2.0 kg bucket straight up, accelerating it from rest at 2.2 m/s2 for 3.0 s.
a. Calculate. the displacement of the bucket. (9.9 m)
= -190 J, F.*-240J)
b. Calculate the work done by each force acting on the bucket. (F,
c. Calculate the total mechanical work done on the bucket. (44 J)
d. Calculate the net force acting on the bucket and the work done by the net force. Compare your answer to the total mechanical
work done on the bucket as calculated in (C). (4.4 N)
5. The graph in Figure 11 shows the force acting on a cart from a spring. The force from the spring is either in the same irection as the
cart's displacement or in the opposite direction.
a. Calculate the work done in sections A, B, and C. (10 J, 2.5 J, -2.5 J)
b. Calculate the total work done. (10 J)
c. Explain why the work done in section C must be negative.
-B
3
Z.SJ -2ST
C
2.CS
10
> -uSS
c) -m pos

Gravitational Potential Energy Practice 6. A 1300-kg car moves from point Ato point B and then to point C. Calculate: a. the gravitational energy at B and at C relative to A (127 530 J, —318 825 J) b. the change in gravitational energy between B and C (-446 355 J) ((300 10m 25 m 7. are used to make a retainingwall in a backyard. Each row of the wallwill contain 10 blocks. You may assume that the first block is placed at the reference level. How much gravitational potential energy is stored in the wall when the blocks are set in place? (235 J) 20k} wove h, -O 0.2 n B. A large slide is shown in Figure 8. A person with a mass of 42 kgstarts from rest on the slide at position A and then slides down to positions B, C, and D. Complete the following using the ground as the reference level Calculate the gravitational potential energy of the person at position A. ( a) The person has a gravitational potential energy of 4500 at position B. How high above the ground is the person at position B? b) The person loses 4900 J of gravitational potential energy when she moves from A to C. How high is the person at C? (10.9 m) c) What is the person's gravitational potential energy at ground level at D? 14.1 m) LfSöOS .81 me) 160m. 

Scene 4

Gravitational Potential Energy Practice
6. A 1300-kg car moves from point Ato point B and then to point C. Calculate:
a. the gravitational energy at B and at C relative to A (127 530 J, —318 825 J)
b. the change in gravitational energy between B and C (-446 355 J)
((300
10m
25 m
7. are used to make a retainingwall in a backyard. Each row of the wallwill contain 10 blocks. You may
assume that the first block is placed at the reference level. How much gravitational potential energy is stored in the wall when the
blocks are set in place? (235 J)
20k}
wove h, -O 0.2 n
B. A large slide is shown in Figure 8. A person with a mass of 42 kgstarts from rest on the slide at position A and then slides down to
positions B, C, and D. Complete the following using the ground as the reference level
Calculate the gravitational potential energy of the person at position A. (
a) The person has a gravitational potential energy of 4500 at position B. How high
above the ground is the person at position B?
b) The person loses 4900 J of gravitational potential energy when she moves from
A to C. How high is the person at C? (10.9 m)
c) What is the person's gravitational potential energy at ground level at D? 14.1 m)
LfSöOS
.81 me)
160m

Work & Potential Energy - Key