Force What is a force? Colloquial understanding of a force – a push or a pull Forces can have different nature Forces are vectors Several forces can act on a single object at a time – they will add as vectors
Chapters 5, 6 Force and Laws of Motion Newtonian mechanics
Describes motion and interaction of objects Applicable for speeds
much slower than the speed of light Applicable on scales much
greater than the atomic scale Applicable for inertial reference
frames frames that dont accelerate themselves Sir Isaac Newton
(1643 1727) Force What is a force? Colloquial understanding of a
force a push or a pull Forces can have different nature Forces are
vectors Several forces can act on a single object at a time they
will add as vectors Force superposition Forces applied to the same
object are adding as vectors superposition The net force a vector
sum of all the forces applied to the same object Newtons First Law
If the net force on the body is zero, the bodys acceleration is
zero Newtons Second Law If the net force on the body is not zero,
the bodys acceleration is not zero Acceleration of the body is
directly proportional to the net force on the body The coefficient
of proportionality is equal to the mass (the amount of substance)
of the object Newtons Second Law SI unit of force kg*m/s 2 = N
(Newton) Newtons Second Law can be applied to all the components
separately To solve problems with Newtons Second Law we need to
consider a free-body diagram If the system consists of more than
one body, only external forces acting on the system have to be
considered Forces acting between the bodies of the system are
internal and are not considered Chapter 5 Problem 14 Three forces
acting on an object are given by F 1 = ( 2.00^i ^j) N, F 2 =
(5.00^i 3.00^j) N, and F 3 = (45.0^i) N. The object experiences an
acceleration of magnitude 3.75 m/s 2. (a) What is the direction of
the acceleration? (b) What is the mass of the object? Newtons Third
Law When two bodies interact with each other, they exert forces on
each other The forces that interacting bodies exert on each other,
are equal in magnitude and opposite in direction Forces of
different origins Gravitational force Normal force Tension force
Frictional force (friction) Drag force Spring force Gravity force
(a bit of Ch. 13) Any two (or more) massive bodies attract each
other Gravitational force (Newton's law of gravitation)
Gravitational constant G = 6.67*10 11 N*m 2 /kg 2 = 6.67*10 11 m 3
/(kg*s 2 ) universal constant Gravity force at the surface of the
Earth g = 9.8 m/s 2 Gravity force at the surface of the Earth The
apple is attracted by the Earth According to the Newtons Third Law,
the Earth should be attracted by the apple with the force of the
same magnitude Weight Weight (W) of a body is a force that the body
exerts on a support as a result of gravity pull from the Earth
Weight at the surface of the Earth: W = mg While the mass of a body
is a constant, the weight may change under different circumstances
Tension force A weightless cord (string, rope, etc.) attached to
the object can pull the object The force of the pull is tension ( T
) The tension is pointing away from the body Free-body diagrams
Normal force When the body presses against the surface (support),
the surface deforms and pushes on the body with a normal force ( n
) that is perpendicular to the surface The nature of the normal
force reaction of the molecules and atoms to the deformation of
material Normal force The normal force is not always equal to the
gravitational force of the object Free-body diagrams Chapter 5
Problem 28 Two objects are connected by a light string that passes
over a frictionless pulley as shown. Draw free-body diagrams of
both objects. Assuming the incline is frictionless, m 1 = 2.00 kg,
m 2 = 6.00 kg, and = 55.0 find (a) the accelerations of the
objects, (b) the tension in the string. Frictional force Friction (
f ) - resistance to the sliding attempt Direction of friction
opposite to the direction of attempted sliding (along the surface)
The origin of friction bonding between the sliding surfaces
(microscopic cold-welding) Static friction and kinetic friction
Moving an object: static friction vs. kinetic Friction coefficient
Experiments show that friction is related to the magnitude of the
normal force Coefficient of static friction s Coefficient of
kinetic friction k Values of the friction coefficients depend on
the combination of surfaces in contact and their conditions
(experimentally determined) Free-body diagrams Chapter 5 Problem 42
Three objects are connected on a table. The rough table has a
coefficient of kinetic friction of The objects have masses of 4.00
kg, 1.00 kg, and 2.00 kg, as shown, and the pulleys are
frictionless. Draw a free-body diagram for each object. (a)
Determine the acceleration of each object and their directions. (b)
Determine the tensions in the two cords. Drag force Fluid a
substance that can flow (gases, liquids) If there is a relative
motion between a fluid and a body in this fluid, the body
experiences a resistance (drag) Drag force ( R ) R = DAv 2 D - drag
coefficient; fluid density; A effective cross-sectional area of the
body (area of a cross- section taken perpendicular to the
velocity); v - speed Terminal velocity When objects falls in air,
the drag force points upward (resistance to motion) According to
the Newtons Second Law ma = mg R = mg DAv 2 As v grows, a
decreases. At some point acceleration becomes zero, and the speed
value riches maximum value terminal speed DAv t 2 = mg Terminal
velocity Solving DAv t 2 = mg we obtain v t = 300 km/h v t = 10
km/h Drag force proportional to speed In dense fluids (liquids) a
resistance force can be proportional to speed b depends on the
property of the medium, and on the shape and dimensions of the
object The negative sign indicates that the force is in the
opposite direction to motion Spring force (a bit of Ch. 7) Spring
in the relaxed state Spring force (restoring force) acts to restore
the relaxed state from a deformed state Hookes law For relatively
small deformations Spring force is proportional to the deformation
and opposite in direction k spring constant Spring force is a
variable force Hookes law can be applied not to springs only, but
to all elastic materials and objects Robert Hooke (1635 1703)
Centripetal force For an object in a uniform circular motion, the
centripetal acceleration is According to the Newtons Second Law, a
force must cause this acceleration centripetal force A centripetal
force accelerates a body by changing the direction of the bodys
velocity without changing the speed Centripetal force Centripetal
forces may have different origins Gravitation can be a centripetal
force Tension can be a centripetal force Etc. Centripetal force
Centripetal forces may have different origins Gravitation can be a
centripetal force Tension can be a centripetal force Etc. Free-body
diagram Chapter 6 Problem 14 A roller-coaster car has a mass of 500
kg when fully loaded with passengers. (a) If the vehicle has a
speed of 20.0 m/s at point A, what is the force exerted by the
track on the car at this point? (b) What is the in maximum speed
the vehicle can have at point B and still remain on the track?
Answers to the even-numbered problems Chapter 5 Problem 2 (a) 1/3;
(b) m/s 2 Answers to the even-numbered problems Chapter 5 Problem 6
(a) 534 N down; (b) 54.5 kg Answers to the even-numbered problems
Chapter 5 Problem 18 (b) 1.03 N; (c) N to the right Answers to the
even-numbered problems Chapter 5 Problem ; 0.245 Answers to the
even-numbered problems Chapter 6 Problem N horizontally inward
Answers to the even-numbered problems Chapter 6 Problem 4 (a) 1.65
km/s; (b) 6.84 10 3 s Answers to the even-numbered problems Chapter
6 Problem 12 (a) 1.33 m/s 2 ; (b) 1.79 m/s 2 forward and 48.0
inward Answers to the even-numbered problems Chapter 6 Problem 26
(a) 6.27 m/s 2 ; (b) 784 N up; (c) 283 N up Answers to the
even-numbered problems Chapter 6 Problem N
