Classical Mechanics Review 1

Midterms: Place, Rules, How to study PLACE AND TIME: Friday, June 2nd, we have the first midterm, covering Units 1-5. All

midterms will be during regular class hours but will take place in the FMAB auditorium (Film and Media Arts Building) which is located south of the Marriott Library - check it out on the campus map. If possible, please be there at least 10 minutes before 11:45 am, so you can get seated, get your exam, fill out all the required information and be ready to start working on problems.

IMPORTANT-PLEASE NOTE THE EXAM RULES: 1. You must bring your University ID to take the exam. 2. You need to bring a pen or two. If you write with a pencil you will not be able to request a

regrade. 3. Bring a scientific/graphing calculator. Devices that can store text are not allowed. 4. Bring a 4"x 6" card with formulas or anything you want. You can write on both sides.

HOW TO PREPARE FOR THE EXAM: 1. Go back and review the Homework assignments and make sure you know how to do them

from scratch on your own. 2. Study this Review for Midterm 1 which will be posted on the main course website and

includes many of the examples from the lectures. 3. Look at old exams and solutions on the main course website: click on "Old exam reviews".

Mechanics Review 1, Slide 1

Classical Mechanics Review 1: Units 1-5


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?

Mechanics Unit 2, Slide 3

Answer:xf = 89.3 m, yf = -62.5 md = 109 m, t = 3.57 s

Example: Stone thrown from a building A stone is thrown from the top of a building 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 to reach the ground? What is the direction of motion (velocity) of the stone just before it hits the ground?


A: t = 4.22 sA: θ = tan-1(-31.4/17.3)

Example A particle starts from the origin at t = 0 with an initial

velocity having an x component of 20 m/s and a y component of -15 m/s. The particle moves in the x-y plane with only an x component of acceleration, given by ax = 4.0 m/s2.

(a) Determine the velocity at any time t. (b) Calculate the speed and direction of motion of the

particle at t = 5.0 s. A: v = 43 m/s, θ = - 21o

(c) Determine the x and y coordinates of the particle at any time t.


Example: Ferris Wheel

A typical carnival Ferris wheel has a radius of 9.0 m and rotates 4.0 times per minute.

(a) What is the period T of the Ferris wheel? A: T =15 s (b) What is the speed of the riders? A: v = 6π/5 m/s (c) What magnitude acceleration do the riders

experience? A: a = 4π2/25 m/s


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2

Example: Three forces

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?


Example: Hockey Puck

A hockey puck of mass 0.30 kg, slides on the horizontal frictionless surface of an ice rink. Two hockey sticks strike it at the same time as shown. Determine the magnitude and the direction of the puck’s acceleration.


A: a = 34 m/s2

A: θ = 310

Example: Two Blocks Two blocks of masses m1 and m2 , are placed in contact with

each other on a frictionless horizontal surface. A constant horizontal force F is applied to m1.

A) Find the acceleration of the blocks. B) Determine the magnitude of the contact force between the

two blocks.


Example: Three Boxes Three boxes of masses mA , mB and mC are on a frictionless

table, connected by massless strings. A unknown force T1

pulls on the rightmost box (A) such that the three boxes accelerate at a rate of a.

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 10

Example: Two Masses and a Pulley

A cart with mass m2 is connected to a mass m1 using a string that passes over a frictionless pulley, as shown below. Initially, the cart is held motionless, but is then released and starts to accelerate.

Find the acceleration of the masses and the tension in string.


m2

m1

a

a

Example: Connected Objects A block of mass m1 on a frictionless horizontal surface 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. Find the normal force on m1.


21

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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.

Mechanics Review 1 , Slide 13

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aT

a

T

m1m2

gmmmma

21

21

gmmmmT

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212

Example: Car on a Slope

A car of mass m is on an icy driveway inclined at an angle θ. Find the acceleration of the car assuming the driveway is frictionless.


Example: Book and Coffee Cup

A book of mass mb is connected by a light string to a coffee cup of mass mc. The book is launched up the frictionless slope of angle θ with an initial speed vi.

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: 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: n = 2.91 x mg

B. Determine the force exerted by the seat on the pilot at the top of the loop. A: n = 0.91 x mg


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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


rgv2

1tan

rv /

rva

2

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Classical Mechanics Review 1