Transcript Lecture 7

Physics I
95.141
LECTURE 7
9/27/10
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Exam Prep Problem
• A 2kg mass sits on a frictionless table, travelling

vo  4iˆ  8 ˆj at t=0. A
with an initial velocity

constant Force of F  4iˆ  2 ˆj is applied to this
mass at t=0.
– A) (5pts) What is the acceleration of the mass for
t>0s?
– B) (5pts) At what time does the y component of
velocity go to 0?
– C) (5pts) At what time does the x component of
velocity go to 0?
– D) (10pts) What is the displacement of the mass
after 5s?
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Exam Prep Problem
• A 2kg mass sits on a frictionless table, travelling

vo  4iˆ  8 ˆj at t=0. A
with an initial velocity

constant Force of F  4iˆ  2 ˆj is applied to this
mass at t=0.
– A) (5pts) What is the acceleration of the mass for
t>0s?
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Exam Prep Problem
• A 2kg mass sits on a frictionless table, travelling

vo  4iˆ  8 ˆj at t=0. A
with an initial velocity

constant Force of F  4iˆ  2 ˆj is applied to this
mass at t=0.
– B) (5pts) At what time does the y component of
velocity go to 0?
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Exam Prep Problem
• A 2kg mass sits on a frictionless table, travelling

vo  4iˆ  8 ˆj at t=0. A
with an initial velocity

constant Force of F  4iˆ  2 ˆj is applied to this
mass at t=0.
– C) (5pts) At what time does the x component of
velocity go to 0?
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Exam Prep Problem
• A 2kg mass sits on a frictionless table, travelling

vo  4iˆ  8 ˆj at t=0. A
with an initial velocity

constant Force of F  4iˆ  2 ˆj is applied to this
mass at t=0.
– D) (10pts) What is the displacement of the mass
after 5s?
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Force Review Problem
• Superman must stop a 4x105kg train traveling at
80m/s in 320m.
• What Force must he exert to do this?
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Outline
• Force of Gravity and Normal Force
• Free Body Diagrams
• Problem Solving
• What do we know?
–
–
–
–
–
–
–
–
Units
Kinematic equations
Freely falling objects
Vectors
Kinematics + Vectors = Vector Kinematics
Relative motion
Projectile motion
Newton’s Laws
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Force of Gravity
• We know that, ignoring air resistance, all objects
dropped near the surface of the Earth will
accelerate with g  9.8 m s
2
• If something is accelerating, that means there must be a
force on it. In this case, that Force is the gravitational
force.
• Magnitude of this force is known as weight.
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Example Problem I(a)
• A upwards Force is exerted on a mass of 2kg.
What is the acceleration of the mass if the Force
is
• A) 10N?
2kg
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Example Problem I(b)
• A upwards Force is exerted on a mass of 2kg.
What is the acceleration of the mass if the Force
is
• B) 19.6N?
2kg
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Example Problem I(c)
• A upwards Force is exerted on a mass of 2kg.
What is the acceleration of the mass if the Force
is
• C) 40N?
2kg
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Force of Gravity
• This force is always acting on objects at the surface of
the Earth.
• Why don’t we see everything accelerating downwards
towards the center of the Earth?
• There is another force acting on the object. And since
the acceleration of the resting object is 0, this force must
be equal to the Force of gravity.
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
The Normal Force
• The Normal Force acts perpendicular to the
surface exerting it. Normal=perpendicular.
• The Normal Force is NOT always vertical. It is
perpendicular to the surface. If the surface is
not horizontal, the Normal Force isn’t vertical.
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Example II(a)
• For a mass M at rest on a flat surface, we can
determine the Normal Force for 3 different
situations:
• A) Box on flat surface
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Example II(b)
• For a mass M at rest on a flat surface, we can
determine the Normal Force for 3 different
situations:
• B) Box on flat surface, hand pushing down -FH
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Example II(c)
• For a mass M at rest on a flat surface, we can
determine the Normal Force for 3 different
situations:
• C) Box on flat surface, hand pulling up +FH<mg
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Solving Force Problems
• FREE BODY DIAGRAMS
– If we are interested in the motion of an object, then
we need to know the NET FORCE acting on that
object!!
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Example Problem III
• My kids are fighting over a 0.5kg
 toy resting on a table (xy plane).
ˆ  3 ˆj N
i
• My son pulls with a force: FS  2

and my daughter with a force of:
FD  1iˆ  2 ˆj N
Find the net Force on the object, and its acceleration.

• Draw Free Body Diagram
• Find Net Force
• Find Acceleration
95.141, F2010, Lecture 7
Department of Physics and Applied Physics



Comments on Example Problem III
• What happened to the Normal Force and the
Force of gravity in this problem?
• What about friction, air resistance, etc.?
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Example IV
• Two boxes are held together by a cable and
pulled by a string on a frictionless table.
• A) Find acceleration of each box
• B) Tension in cord
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Example IV
• Choose coordinate system
• Free Body Diagrams for each box
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Example IV
• How do we handle the connecting (massless) cord?
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Example IV
• Sum Forces
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Example IV
• Solve system of equations
F
xB
 T  mB a xB
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
F
xA
 40 N  T  m Aa xA
Free Body Diagrams
• For any object subject to a Force, we can always
draw a free body diagram.
• When we choose coordinate system, we want to
choose carefully…
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Boxes on Inclines
• Now suppose we have a box of mass M on a
frictionless inclined plane…
– Coordinate system
θ
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Boxes on Inclines
• Now suppose we have a box of mass M on a
frictionless inclined plane…
– Free Body Diagram
θ
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Boxes on Inclines
• Divide Forces into x, y components

FN
θ

Fgy
Φ
95.141, F2010, Lecture 7
Department of Physics and Applied Physics

Fgx

Fg
Boxes on Inclines
• What is Φ?
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Boxes on Inclines
• Divide Forces into x, y components

FN
θ

Fgy
θ

Fgx

Fg
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Example V
• A 10 kg box sits on a frictionless inclined plane
(θ=30º).
– What is the Normal Force on the box?
– What is the box’s acceleration?
• Draw diagram and choose coordinate system
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Example V
• A 10 kg box sits on a frictionless inclined plane
(θ=30º)
• Free body diagram
• Divide Forces into x, y
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Example V
• A 10 kg box sits on a frictionless inclined plane
(θ=30º)
• Solve for acceleration
95.141, F2010, Lecture 7
Department of Physics and Applied Physics
Problem Solving approach
•
•
•
•
•
•
Draw Diagram
Choose coordinate system
Draw Free Body Diagram
Determine Force components
Write equations of motion
Solve
95.141, F2010, Lecture 7
Department of Physics and Applied Physics