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PHYSICS 13 & 11AGENERAL PHYSICS 1
MARLON FLORES SACEDON
Dynamics of Motion:Application of Newtonโs Laws of Motion
Friction ๐ - refers to actual forces that are exerted to oppose motion- a resistance that opposes every effort to slide or roll a body over another
Kinds of Friction:1. Static friction - force that will just start the body.2. Kinetic friction - force that will pull the body uniformly.
APPLICATION OF NEWTONโS LAWS OF MOTION
Friction
Coefficient of friction ๐ - the ratio of the force necessary to move one surface over the other with uniform velocity to the normal force pressing the two surfaces to other.
๐ =๐
๐ Where: N is the normal force exerted by the contact surface to the object.
m
๐
๐
๐ค
๐
๐
๐ฆ
๐ฅ
๐
๐ = ๐๐
Free-Body Diagram (FBD)
m
๐
๐
๐ค
๐
๐
๐ฆ
๐ฅ
๐
FBD is a vectors diagram showing all forces acting on the body.
APPLICATION OF NEWTONโS LAWS OF MOTION
Free-Body Diagram (FBD)
FBD of Furniture
๐ฆ
๐ฅ
๐ฎ๐ญ๐
๐ท
๐ = ๐๐
N
๐ = ๐๐ต
ฮฃ ๐น๐ฆ = ๐ โ ๐ค = 0 (for static equilibrium)ฮฃ ๐น๐ฅ = ๐ โ ๐ (Net External force)
๐ฎ๐ญ = ๐๐ฅ โ ๐
Net external force
Note: If pulling force ๐ is less than friction ๐then furniture is at rest otherwise it will move to the right..
APPLICATION OF NEWTONโS LAWS OF MOTION
FBD is a vectors diagram showing all forces acting on the body.
Free-Body Diagram (FBD)
N
P
๐ = ๐๐
๐ฆ
๐ฅ
๐ท๐
๐ท๐
FBD of box
ฮฃ ๐น๐ฆ = ๐ + ๐๐ฆ โ ๐ค = 0 (for static equilibrium)
๐ = ๐๐ต
ฮฃ ๐น๐ฅ = ๐๐ฅ โ ๐ (Net External force)
๐ฎ๐ญ = ๐๐ฅ โ ๐
Note: If ฮฃ ๐น๐ฆ is not equal to zero then box didnโt touch the ground surface. Therefore Net external force is not equal to ฮฃ ๐น๐ฅ.
Net external force
๐ฎ๐ญ๐
APPLICATION OF NEWTONโS LAWS OF MOTION
FBD is a vectors diagram showing all forces acting on the body.
Free-Body Diagram (FBD)
Exercise Problem: Construct the free-body diagram (FBD)
๐ = ๐๐
FBD of box
๐๐
๐๐20๐
APPLICATION OF NEWTONโS LAWS OF MOTION
๐ ๐ก = 2๐
๐๐ด
๐๐ต
Problem: A horizontal cord is attached to a 6.0-kg body in a horizontal table. The cord passes over apulley at the end of the table and to this end is hung a body of mass 8 kg. Find the distance the twobodies will travel after 2s, if they start from rest. What is the tension in the cord?
Figure:
๐๐ด
๐๐ต
๐๐ต
๐๐ด
๐
๐ก = 2๐
APPLICATION OF NEWTONโS LAWS OF MOTION
๐๐ต
๐๐ด
๐ ๐ก = 2๐
๐๐ด
๐๐ต
Problem: A horizontal cord is attached to a 6.0-kg body in a horizontal table. The cord passes over apulley at the end of the table and to this end is hung a body of mass 8 kg. Find the distance the twobodies will travel after 2s, if they start from rest. What is the tension in the cord?
Figure:
๐๐ด
๐๐ต
๐
๐ก = 2๐
๐ฆ
๐ฅ
๐ฆ
๐ฅ๐๐ด๐ฆ
๐ฅ
๐๐ต
+๐๐๐๐๐
โ๐๐๐๐๐
โ๐ค๐ด= ๐๐ด๐
๐ค๐ต = ๐๐ต๐
๐ฮฃ ๐น๐ด
ฮฃ ๐น๐ต
๐
๐
FBD of ๐๐ด FBD of ๐๐ต
ฮฃ ๐น๐ฅ = +๐๐๐๐๐
ฮฃ ๐น๐ฆ = ๐ โ ๐ค๐ด = 0 (static equilibrium)
ฮฃ ๐น๐ด = ๐๐ด๐From Second law
๐๐๐๐๐ = ๐๐ด๐ Eq.1
ฮฃ ๐น๐ฆ = 0 (static equilibrium)
ฮฃ ๐น๐ฅ = โ๐๐๐๐๐+๐๐ต๐
ฮฃ ๐น๐ต = ๐๐ต๐From Second law
โ๐๐๐๐๐+๐๐ต๐ = ๐๐ต๐ Eq.2
Contโn
Add ๐ธ๐ 1and ๐ธ๐. 2 to eliminate
๐๐๐๐๐ then solve Acceleration ๐.
๐ =๐๐ต๐
๐๐ด + ๐๐ต๐ =
8(9.81)
6 + 8= 5.61๐/๐ 2
Net external force
Net external force
APPLICATION OF NEWTONโS LAWS OF MOTION
๐๐ต
๐๐ด
๐ ๐ก = 2๐
๐๐ด
๐๐ต
Problem: A horizontal cord is attached to a 6.0-kg body in a horizontal table. The cord passes over apulley at the end of the table and to this end is hung a body of mass 8 kg. What is the tension in thecord? Find the distance the two bodies will travel after 2s, if they start from rest.
Figure:
๐๐ด
๐๐ต
๐
๐ก = 2๐
๐ฆ
๐ฅ
๐ฆ
๐ฅ
a) Solve for tension in the cord ๐๐๐๐๐ using Eq.1
๐๐๐๐๐ = 6(5.61)=33.66 N ANSWER
b) Solve for the distance ๐ of two bodies after travelling 2 sec.
Given:
๐ฃ๐ = 0
๐ก = 2 ๐ ๐ = 5.61 ๐/๐ 2
From kinematics: ๐ = ๐ฃ1๐ก +1
2๐๐ก2
๐ = 0 2 +1
25.61 22 = 11.22๐ ANSWER
APPLICATION OF NEWTONโS LAWS OF MOTION
. Given:
m = 10 kg
h = 5 m
L = 10m
S1 = 2m
ร =44o
๐ = 0.06 coef. of kinetic frictionNote:
Particle โmโ is release from rest at pt. A and moves
to pt. B, then to pt.C, and finally to pt.D.
Neglect the effect of the change in velocity direction at pt.B.
The same value of coef. friction, from pt.A to pt.C.
Projectile motion from pt.C to pt.D.
Required:
a. Free-body diagram of the particle at inclined plane AB.
b. Free-body diagram of the particle at horizontal plane BC.
c. Unbalanced force of the particle along the inclined plane AB.
d. Unbalanced force of the particle along the horizontal plane BC.
e. acceleration, a1 of the particle along the inclined plane AB.
f. acceleration, a2 of the particle along the horizontal plane BC.
g. velocity of the particle at pt.B.
h. velocity of the particle at pt.C.
i. Range, (S2)
j. Total time of travel of particle from pt A to pt. D.
ASSIGNMENT
Figure:
ASSIGNMENT
ASSIGNMENT
ASSIGNMENT
eNd
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