1. Purdue University, Physics 220
Lecture 04
Forces and Motion in 1 D
Textbook Sections
Lecture 4
Purdue University, Physics 220

2. Graphing calculator are not allowed during exams.
Because they it can store nearly everything in memory.
Lecture 3
Purdue University, Physics 220

3. Purdue University, Physics 220
Mass and Weight
Mass: quantifies the amount of inertia that an object possesses – an intrinsic property of the object
Weight (Gravitational force exerted by the Earth)
W = mg (g-acceleration due to gravity)
g = GMearth/(rearth)2 = 9.8 m/s2
(G – universal gravitational constant, more in Chapter 5)
Lecture 4
Purdue University, Physics 220

4. Purdue University, Physics 220
Contact Forces
Normal force: a contact force acting at an interface
perpendicular to the surface of contact
Frictional force: another contact force acting at an interface
parallel to the surface of contact
resist motion of the two surfaces sliding past each other
always act opposite the direction of motion mg N F Ff
Lecture 4
Purdue University, Physics 220

5. Purdue University, Physics 220
Friction
Magnitude of frictional force is proportional to the normal force.
Fkinetic = mk N mk coefficient of kinetic friction
Fstatic  ms N ms coefficient of static friction
Be Careful!
Static friction , can be any value up to msN
Direction always opposes motion
Lecture 4
Purdue University, Physics 220

6. Friction and Walking The person “pushes” off during each step
The bottoms of his shoes exert a force on the ground
If the shoes do not slip, this force is due to static friction
The shoes do not move relative to the ground

7. Book Pushed Across Table
Book sliding across table
Isolate the object of interest (book)
Identify all forces acting on the object
Hand (to right)
Gravity (down)
Normal (table, up)
Friction (table, left)
Choose a coordinate system y x
Normal
friction
hand
Gravity
Physics
Lecture 4
Purdue University, Physics 220

8. Purdue University, Physics 220
Contact Force: Spring
Force exerted by a spring is directly proportional to the amount by which it is stretched or compressed. Fspring = k x always trying to restore its original length
Example: When a 5 kg mass is suspended from a spring, the spring stretches 8 cm. Determine the spring constant.
Fspring
Fspring- Fgravity = 0
Fspring = Fgravity
k x = m g
k = m g / x
= (5 kg) x (9.8 m/s2) /(0.08 m)
= 612 N/m
Maybe simple demo, add twice as much mass, get twice the stretching before showing the slide. Also make note that this is NOT as big a deal as Newton’s laws. Just an example of a contact force.
Fgravity y x
Lecture 4
Purdue University, Physics 220

9. Contact Force: Tension
A force transmitted by a rope, cord, cable or the like which transmits a force from one end to an object attached at the other end
Ideal string (or cord, rope, etc.):
Always maintains constant tension everywhere.
Has a zero mass.
Tension is parallel to the string
Pulley changes the direction of the force
associated with the tension in the rope.
Lecture 4
Purdue University, Physics 220

10. Purdue University, Physics 220
iClicker
Two boxes are connected by a string over a frictionless pulley. In equilibrium, box 2 is lower than box 1. Compare the weight of the two boxes.
A) They have the same weight
B) Box 1 is heavier
C) Box 2 is heavier 1 T
m1g 1
SF = 0
1) T - m1 g = 0
2) T – m2 g = 0
=> m1 = m2 2 T
m2g 2
Lecture 4
Purdue University, Physics 220

11. Purdue University, Physics 220
Tension Example
Determine the force exerted by the hand to suspend the 45 kg mass as shown in the picture.
1) 220 N 2) 440 N 3) 660 N
4) 880 N 5) 1100 N y x T T
SF = 0
T + T – W = 0
2 T = W
T = m g / 2
= (45 kg x (9.8 m/s2)/ 2
= 220 N W
Remember the magnitude of the tension is the same everywhere along the rope!
Lecture 4
Purdue University, Physics 220

12. Purdue University, Physics 220
Question
What is the force on the ceiling? y x
A) 220 N B) 440 N C) 660 N
D) 880 N E) 1100 N
SF = 0
Fc -T - T – T = 0
Fc = 3 T
Fc = 3 x 220 N = 660 N Fc T
Lecture 4
Purdue University, Physics 220

13. Purdue University, Physics 220
Question
What does the scale read?
A) 225 N B) 550 N C) 1100 N
The sum of the forces here will be 0. Thus, the force tension will equal the force gravity. Since the force of gravity is 550N, the force of tension (which is measured by the scale) will also be 550N.
Lecture 4
Purdue University, Physics 220 30

14. Purdue University, Physics 220
Pulley Example
Two boxes are connected by a string over a frictionless pulley. Box 1 has mass 1.5 kg, box 2 has a mass of 2.5 kg. Box 2 starts from rest 0.8 meters above the table, how long does it take to hit the table.
Compare the acceleration of boxes 1 and 2
A) |a1| > |a2| B) |a1| = |a2| C) |a1| < |a2|
1) T - m1 g = m1 a1
2) T - m2 g = -m2 a1
using a1 = -a2
2) T = m2 g -m2 a1
1) m2 g -m2 a1 - m1 g = m1 a1
a1 = (m2 – m1)g / (m1+m2) y x 1
Do this on transparency 1 T
m1g 2 T
m2g 2
Lecture 4
Purdue University, Physics 220

15. Purdue University, Physics 220
Pulley Example
Two boxes are connected by a string over a frictionless pulley. Box 1 has mass 1.5 kg, box 2 has a mass of 2.5 kg. Box 2 starts from rest 0.8 meters above the table, how long does it take to hit the table.
a1 = (m2 – m1)g / (m1+m2)
a = 2.45 m/s2
Dx = v0t + ½ a t2
Dx = ½ a t2
t = sqrt(2 Dx/a)
t = 0.81 seconds y x 1
Do this on transparency 1 T
m1g 2 T
m2g 2
Lecture 4
Purdue University, Physics 220

16. Purdue University, Physics 220
Free Fall
At the earth’s surface freely falling bodies experience a constant acceleration of 9.8 m/s2
There is a choice of axes:
1) Choose positive y up in which case a=g=-9.8 m/s2
2) Choose positive y down in which case a=g=9.8 m/s2 y
g=9.8 m/s2
Lecture 4
Purdue University, Physics 220

17. Purdue University, Physics 220
Free Fall
Only force acting on object is GRAVITY
Newton’s 2nd Law Fy = may
Force is Weight = mg (near surface of earth)
-mg = may
ay = -g (- sign tells us it is in –y direction or down)
Acceleration is always g downwards
Velocity may be positive, zero or negative
Position may be positive, zero or negative y x
Demos penny and feather. First with air resistance, then without.
y = y0 + vy0t - 1/2 gt2
vy = vy0 - gt
vy2 = vy02 - 2g(y-y0)
Lecture 4
Purdue University, Physics 220

18. Purdue University, Physics 220
Example of Free Fall
This is for y0=0 and v0=0
Lecture 4
Purdue University, Physics 220

19. Purdue University, Physics 220
iClicker
Fred throws a ball 30 mph vertically upward and then catches it again at the same height he threw it from. What is the speed of the ball when he catches it? (Neglect air resistance)
A) v = 30 mph B) v < 30 mph C) v > 30 mph
vy2 = vy02 - 2g(y-y0)
vy2 = vy02
Lecture 4
Purdue University, Physics 220

20. Two blocks one sliding one hanging
A block of mass m1=3kg rests on a frictionless horizontal surface. A second block of mass m2=2kg hangs from an ideal cord of negligible mass who runs over an ideal pulley. Block 2 starts from rest 0.8 meters above the floor, how long does it take to hit the floor? a a
a1 = (m2 )g / (m1+m2)
a = 3.9 m/s2
y = v0t + ½ a t2= ½ a t2
t = sqrt(2 y/a)
t = 0.64 seconds
Lecture 4
Purdue University, Physics 220