Transcript AP C UNIT 2 - student handout

APC -Unit 2
2nd Law
A 72kg person stands on a scale which sits on a
floor of elevator. It starts to move from rest
upward with speed v(t) = 3t + 0.2t2,
a) find scale reading at t = 4.0s.
b) If elevator is at x =10m when t =2.0s, find location
at t = 4.0s
Equilibrium
When net force in all directions is zero
60o
A
30o
B
15N
Find the tension
in cable A and B
A circus performer of weight W is walking along a
"high wire" as shown. The wire bends and makes a
shallow angle below the horizontal. The tension in
the wire is:
a) depends on whether he stands on one or two feet
b) much more than W
c) much less than W
d) approximately W/2
e) approximately W
System Acceleration
A block of mass M and a block of mass m are connected by
a thin string that passes over a light frictionless pulley. Find
the acceleration of the system using only variables and
constants.
Three blocks are connected as shown. Find the
tension in the rope connecting the block on table.
Assume no friction & massless rope.
Find system acceleration
using only variables and
constants.
Now find tension
Find tension in rope on left assuming
smooth table surface
example
An object of mass 5.0 kg is subjected to a rightward
force in newtons of F = 3t2 – 4t where t is measured
in seconds. The object has velocity v = 7.0m/s, left
at t = 2.0s. Determine the velocity & acceleration of
the object at t = 9.0s.
Inclined Plane
Φ θ
θ
θ
A 7.5kg shopping cart is accelerated up the incline at a rate of
1.4m/s2. Incline is angled at 13o and no friction is present.
A)Determine the value of the force, F, in the horizontal direction
(0o) needed to do this.
B)Determine value of normal force on cart
F
The diagram shows four choices for the direction of a force of
magnitude F to be applied to a block on an inclined plane. The
directions are either horizontal or vertical. (For choices a and
b, the force is not enough to lift the block off the plane.) Rank
the choices according to the magnitude of the normal force on
the block from the plane, greatest first.
Friction (f)
A force that acts parallel to surfaces in contact with
one another. Two types are kinetic and static.
FAPP
fs
Static friction > Kinetic friction
Example
20o
A 10 kg box is pulled
with a force of 30N
along a rough floor
(μk = 0.30) as shown.
a) Draw FBD of ALL forces acting on box
b) Determine the acceleration of the box.
Determine the acceleration of the masses
assuming coefficient of kinetic friction is 0.2.
Determine the tension in rope assuming massless.
SLIDING BLOCKS
A 10 kg block rests on top of a 40 kg slab which rests on
a frictionless floor. The coefficient of static and kinetic
friction between the block and the slab are 0.60 and
0.40 respectively. The block is pulled with a force of
100 N. What are the accelerations of (a) the block and
(b) the slab?
*Must first decide on whether the block will slide
relative to the slab?
In random pairs, determine and
submit on paper your answer
with justification.
More Calculus Needed!
d ax
ax
e  ae
dx
1 ax
 e dx  a e  C
1
 x dx  ln x  C
ax
Natural Log properties:
e
ln x
x
ln e  x
x
a
ln  ln a  ln b
b
*u substitution
U-Substitution
There are times when the power rule is not
an option for use as an integration technique.
Example:
For times greater than 0, an object beginning at
the origin moves in one dimension according to
the following expression:
12
v(t ) 
6  7t
Find the distance traveled by the object during the
first 10 seconds.
Differential Equations
An equation that relates a quantity and its derivatives is
called a differential equation. In APC Physics, we only
need to be familiar with a few basic Diff E q’s. The
independent variable will always be time, t.
The acceleration of an object is given by the following
function:
a (t )  32  4v
Derive an expression for the velocity as a function of time
assuming initial conditions are that x = 0 and v = 4m/s at t=0.
EXAMPLE: The acceleration of a particle,
a = –1.2x–0.8x3 and when x = +5m, v = 4m/s.
Determine how far does the particle travel before
coming to rest? (note ‘a’ is given in terms of x)
Integrating
at
e
1 ax
e
dx

e

C

a
ax
2 EXAMPLES
A particle moves in one dimension with a
velocity as follows:
v(t) = 5e-t/2
Find the displacement of the particle from t = 0 to t = 4s.
An object falls from rest from a large distance. Due to
gravity and air drag, the velocity of object follows the
equation: v(t) = 60 (1-e-t/10)
Find an expression for the displacement as a function of time.
Force proportional to v
Consider a mass (m) that experiences a
resistive force of air, F = -bv, where b is
positive constant. Find v as function of t.
Fdrag
Take
down to
be
positive
mg
Air resistance handout
If a force F(t) = Foe-kt acts on mass, m, that is initially at rest,
what is the expression for the final velocity of object as time
approaches infinity?
Bosun Chair
The tension is half
in the picture on the
left of what it is on
the right since chair
is supported by 2
ropes instead of 1
Is there a difference in the tension
in the rope attached to the chair in
the 2 situations? If so, what?
Assume massless, frictionless
pulley & massless rope.
With what force must the man
pull on the rope to rise at
constant speed?
Force
on
rope
Circular Motion
(FNET=ma for circles)
Centripetal Force, FC , is a special way to say FNET
If an object is experiencing uniform circular
motion, is it in equilibrium?
Consider amusement park
ride of the rotating swings.
Swingcars rise into air until
they reach a steady height.
Find the speed of each
swingcar if chain length is
5.0m and the angle btw
vertical and chain is 35o
The RotoRide involves spinning
people in ac circle like the spin
cycle of a washing machine.
Once the ride gets upto speed, the
floor drops and you don’t slide.
Find minimum period for this to
occur assuming the radius of the
ride is R and coefficient of static
friction is uS.
Banked Curve
Force analysis of car
without friction
What force provides
FC on car to be able
to perform circular
motion?
What speed does car
need to execute
curve without friction
assuming radius of
curve is R and angle
of curve is θ?
If friction needs to act (recall friction doesn’t always
need to be present), which direction will it point?