Classical Mechanics Review 1: Units 1-6 Mechanics Review 1, Slide 1

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.


m2gm1g

aT

a

T

m1m2

gmm

mma

21

21

gmm

mmT

21

212

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.

Mechanics Review 1, Slide 3

21

12(sin(cos

mm

mmgFa kk

gmFn 1sin

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


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?


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 sθ = tan-1(-31.4/17.3)

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?


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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


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


rg

v21tan

rv /

r

va

2


Example: Field GoalA 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-direction

voy = vo sin(30o) = 15 m/s

y = yo + voyt + ½ at 2

3 m = 0 m + (15 m/s) t – ½ (9.8 m/s2) t 2

t = 2.8 s or t = 0.22 s.

x-direction

vox = vo cos(30o) = 26 m/s

D = xo + vox t + ½ at 2

= 0 m + (26 m/s)(2.8 s) + 0 m/s2 (2.8 s )2

= 72.8 m

D

3 m

y

x

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.


ck tan

Example: Satellite in Orbit


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?


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Classical Mechanics Review 1: Units 1-6 Mechanics Review 1, Slide 1