PreClass Notes: Chapter 5, Sections 5.1-5 - U of T Physicsjharlow/teaching/... · PreClass Notes:...

2015-07-14

1

© 2012 Pearson Education, Inc. Slide 1-1

PreClass Notes: Chapter 5, Sections 5.1-5.3

• From Essential University Physics 3rd Edition

• by Richard Wolfson, Middlebury College

• ©2016 by Pearson Education, Inc.

• Narration and extra little notes by Jason Harlow,

University of Toronto

• This video is meant for University of Toronto

students taking PHY131.


Outline

• 5.1 Problem Solving with

Newton’s Second Law

• 5.2 Objects Connected by

Ropes and Pulleys

• 5.3 Circular Motion

“Why does an airplane tip when

it’s turning?” – R.Wolfson

Image from http://www.decodedscience.com/side-effect-of-rolling-an-airplane-aircraft-yaw/7209

2015-07-14

2


• Interpret the problem to make sure Newton’s second law is

the relevant concept. Identify which objects are of interest

and think about the forces on each object. Identify

connections between objects and the constraints on their

motion.

• Draw a free-body diagram for each object. Develop your

solution plan by writing Newton’s second law in

components for each object.

• Execute your plan and solve the equations. Remember

that the constraints are like equations.

• Assess your solution to see whether it makes sense.

Think about units, special cases.

Problem Solving Strategy 5.1


Example 5.1

A skier of mass m = 65 kg glides down a

slope at an angle of θ = 32°, as shown.

Find (a) the skier’s acceleration and (b) the

force the snow exerts on the skier. The snow

is so slippery that you can neglect friction.

2015-07-14

3


Example 5.1


Example 5.1

2015-07-14

4


Got it?

• A ball of mass m is suspended by a string from the

ceiling inside an elevator. If the elevator is moving

upward with a constant speed, the tension in the

string

A. is greater than mg.

B. is equal to mg.

C. is less than mg.

D. depends on the speed of the elevator.


Tension

Figure (a) shows a heavy

safe hanging from a rope

The combined pulling force

of billions of stretched

molecular springs is called

tension

Tension pulls equally in both

directions

Figure (b) is a very thin cross

section through the rope

This small piece is in

equilibrium, so it must be

pulled equally from both sides

2015-07-14

5


Example 5.2

To protect her 17 kg pack

from bears, a camper hangs it

from ropes between two trees,

as shown. What’s the tension

in each rope?


Example 5.2

2015-07-14

6


The Massless String Approximation

Often in problems the mass of the string or rope is much

less than the masses of the objects that it connects.

In such cases, we can adopt the following massless string

approximation:


Got it?

• A rope is tied to a hook that is attached to a wall. If

you pull the rope with a 1-N force, the force

exerted by the hook on the rope

A. is greater than 1 N.

B. is less than 1 N.

C. is equal to 1 N.

D. cannot be determined from the information given.

2015-07-14

7


Pulleys

Block B drags block A across a frictionless table as it falls

The string and the pulley are both massless

There is no friction where the pulley turns on its axle

Therefore, TA on S = TB on S


Acceleration Constraints

If two objects A and B move together, their accelerations are

constrained to be equal: aA = aB

This equation is called an acceleration constraint

Consider a car being towed by a truck

In this case, the

acceleration constraint is

aCx = aTx = ax

Because the

accelerations of both

objects are equal, we can

drop the subscripts C and

T and call both of them ax

2015-07-14

8


Acceleration Constraints

Sometimes the acceleration

of A and B may have

different signs

Consider the blocks A and

B in the figure

The string constrains the

two objects to accelerate

together

But, as A moves to the right in the +x direction, B moves

down in the −y direction

In this case, the acceleration constraint is aAx = −aBy


Example 5.4

A 73 kg climber finds himself dangling

over the edge of an ice cliff, as shown.

Fortunately, he’s roped to a 940 kg rock

located 51 m from the edge of the cliff.

Unfortunately, the ice is frictionless, and

the climber accelerates downward.

What’s his acceleration?

2015-07-14

9


Example 5.4


Example 5.4

2015-07-14

10


Dynamics of Uniform Circular Motion

Without such a force,

the object would move

off in a straight line

tangent to the circle.

The car would end

up in the ditch!

An object in uniform circular motion is not traveling at a

constant velocity in a straight line.

Consequently, the particle must have a net force acting

on it


Example 5.6

2015-07-14

11


Example 5.6


Example 5.6

2015-07-14

12


Example 5.6


Example 5.7

The “Dragon Fire” roller coaster at Canada’s Wonderland features a

double loop section. One of the loops is shown, and the radius of

curvature at the top is 6.3 m. What’s the required speed for a roller

coaster at the top of the loop if the normal force from the track is to be

zero (neither pushing nor pulling)?

2015-07-14

13


Example 5.7


Example 5.7

PreClass Notes: Chapter 5, Sections 5.1-5 - U of T Physicsjharlow/teaching/... · PreClass Notes:...

Documents

Transcript of PreClass Notes: Chapter 5, Sections 5.1-5 - U of T Physicsjharlow/teaching/... · PreClass Notes:...