Classical Mechanics
Review 1: Units 1-6
Mechanics Review 1 , Slide 1
Example: Atwood Machine
Two objects of unequal mass are hung vertically over a
frictionless pulley of negligible mass. Determine the
magnitude of the acceleration of the two objects and the
tension in the string.
 m1  m 2 
 g
a  
 m1  m 2 
T
a
m2
T
m1
a
m1g
 2 m1m 2
T  
 m1  m 2

 g

m2g
Mechanics Review 1 , Slide 2
Example: Two Blocks and a Pulley
A block of mass m1 on a horizontal surface with coefficient of
kinetic friction µk, is connected to a ball of mass m2 by a cord
over a frictionless pulley. A force of magnitude F at an angle θ
with the horizontal is applied to the block and the block slides to
the right.
Determine the magnitude of the acceleration of the two objects.
n  F sin   m1 g
 F (cos    k sin   g ( m 2   k m 1
a  
m1  m 2




Mechanics Review 1, Slide 3
Example: Loop the Loop
A pilot of mass m in a jet aircraft executes a loop-the- loop. In
this maneuver the aircraft moves in a vertical circle of radius
2.70 km at a constant speed of 225 m/s.
A. Determine the force exerted by the seat on the pilot at the
bottom of the loop. A: 2.91 mg
B. Determine the force exerted by the seat on the pilot at the
top of the loop. A: 0.913 mg
Mechanics Review 1 , Slide 4
Example: Three Boxes
Three boxes each of mass 14 kg are on a frictionless table,
connected by massless strings. A force T1 pulls on the
rightmost box (A) such that the three boxes accelerate at a
rate of a = 0.7 m/s2 .
1.What is the magnitude of T1?
2. What is the net horizontal force on A?
3. What is the force that box B exerts on A?
4. What is the net force on box B?
5. What is the force box C exerts on B?
Mechanics Review 1, Slide 5
Example: Stone in Free Fall
A stone is thrown from the top of a building upward at an
angle of 30.0o to the horizontal with an initial speed of 20.0
m/s. The height of the building is 45.0 m. How long does it
take the stone to reach the ground? What is the direction of
motion of the stone just before it strikes the ground?
t = 4.22 s
θ = tan-1(-31.4/17.3)
Mechanics Review 1 , Slide 6
Example: Ski Jump
A ski jumper leaves the ski track moving in a horizontal
direction with a speed of 25.0 m/s. The landing incline
below her falls off with a slope of 35.0o. Where does she
land on the incline? What is her speed when she lands?
d  109 m
Mechanics Review 1 , Slide 7
Example: Book and Coffee Cup
The 2.0 kg book is connected by a light string to a 300 g
coffee cup. The book is launched up the frictionless 20o slope
with an initial speed of 5.0 m/s.
A. Calculate the acceleration of the book.
B. How far does the book go up the slope before it stops?
C. Calculate the Tension in the string
Mechanics Review 1 , Slide 8
Example: Banked Curve
A car moving at the designated speed of 13.4 m/s can
negotiate a curve even when the road is covered with ice, if
the ramp is banked (meaning that the roadway is tilted toward
the inside of the curve). The radius of the curve is 50.0 m.
A. What is the angular speed of the car?
B. What is the acceleration of the car?
C. At what angle should the curve be
banked? A: 20.1o
  v/r
a
v
2
r
2

v
1
  tan 
 rg




Mechanics Review 1, Slide 9
Example: Field Goal
A field goal kicker can kick the ball 30 m/s at an angle of 30 degrees w.r.t. the
ground. If the crossbar of the goal post is 3m off the ground, from how far
away can he kick a field goal?
y
x
3m
D
y-direction
x-direction
voy = vo sin(30o) = 15 m/s
vox = vo cos(30o) = 26 m/s
y = yo + voyt + ½ at 2
D = xo + vox t + ½ at 2
3 m = 0 m + (15 m/s) t – ½ (9.8 m/s2) t 2
= 0 m + (26 m/s)(2.8 s) + 0 m/s2 (2.8 s )2
t = 2.8 s or t = 0.22 s.
= 72.8 m
Mechanics Review 1, Slide 10
Example: Block on Incline Plane
Suppose a block is placed on a rough surface inclined relative
to the horizontal. The incline angle is increased until the block
starts to move. Show that you can obtain μs by measuring the
critical angle θc at which this slipping just occurs.
 k  tan  c
Mechanics Review 1, Slide 11
Example: Satellite in Orbit
Mechanics Review 1 , Slide 12
Example: Forces and Inclines
Three forces are exerted on an object placed on an inclined
plane. The three forces are directed as shown in the figure.
The forces have magnitudes F1 = 3.00 N, F2 = 8.00 N and
F3 = 6.00 N.
A. What is the component of the
net force parallel to the incline?
B. What is the component of the net
force perpendicular to the incline?
C. What is the magnitude of the net
force?
Mechanics Review 1 , Slide 13