Download A body acted on by no net force moves with

Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lecture 10
A physics professor did daredevil stunts in his spare
time. His last stunt was an attempt to jump across a
river on a motorcycle. The takeoff ramp was inclined
at 53.00, the river was 40.0 m wide, and the far bank
was 15.0 m lower than the top of the ramp. The river
itself was 100 m below the ramp. You can ignore air
resistance. a) What should his speed have been at the
top of the ramp to have just made it to the edge of the
far bank? b) If his speed was only half the value
found in (a), where did he land?
A faulty model rocket moves in the xy-plane (the positive ydirection is vertically upward). The rocket’s acceleration has
components ax(t)=t2 and ay(t)=-t, where =2.50 m/s4, =9.00
m/s2, and =1.40 m/s3. At
 t=0 the rocket is at the origin and has

velocity v0  v0 x i  v0 y j with v0 x  1.00 m / s and v0 y  7.00 m / s.
a) Calculate the velocity and position vectors as functions of time.
b) What is the maximum height reached by the rocket?
c) What is the horizontal displacement of the rocket when it
returns to y=0?
An object’s acceleration is given by



2
a  ti  t j
If the object starts at t=0 at the origin with an initial
velocity of magnitude Vi directed at θ above the x axis,
what are its velocity and position at any time?
Dynamics
Connection between force and motion
The concept of force gives us a quantitative
description of the interaction between two
bodies or between a body and its environment
Newton’s Laws
1st Law: A body acted on by no net force moves with
constant velocity (which may be zero) and zero acceleration
2nd Law: The acceleration of an object is directly
proportional to the net force acting on it and is inversely
proportional to its mass. The direction of the acceleration
is in the direction of the net force acting on the object.
3rd Law: For every action there is an equal, but
opposite reaction
2nd Law
From experiments we know:
1.Force is a vector
2.The direction of acceleration vector is the
same as the direction of the force vector
3.The magnitude of the force and
acceleration are related by a constant
which depends on number of blocks
involved.
Newton’s second law


F  ma
The vector acceleration of an object is in the same
direction as the vector force applied to the object
and the magnitudes are related by a constant called
the mass of the object.


F  mg
Gravitational force
Normal force
Force exerted by a spring:
Hooke’s law: If spring is stretched or compressed
by some small amount it exerted a force which is
linearly proportional to the amount of stretching
or compressing. The constant of proportionality is
called the spring constant

Fspring  k x ,
x -is
deviation from the natural
length
The force resisting the pull of the spring –
friction
There is some maximum value the friction force can
achieve, and once we apply a force greater than this
maximum there is a net force on the object, so it
accelerates.
The maximum of the force of friction varied linearly
with the amount that the block pushes on the table.


Ffriction   N

 - coefficient of friction, N is the vertical force exerted by
the block on the table
The friction force only exists when there is another
force trying to move an object
A Recipe for Solving Problems
1. Sketch
Isolate the body (only external forces but not forces
that one part of the object exert on another part)
2. Write down 2nd Newton’s law


F  ma
Choose a coordinate system
Write 2nd Newton’s law in component form:





F  Fx i  Fy j  max i  ma y j
Fx  max , Fy  ma y
3. Solve for acceleration
Have a great day!
Reading: Chapter 5,6
Hw: Chapter 6 problems and
exercises