physics 1d03 - lecture 81 newton’s laws (iv) blocks, ramps, pulleys and other problems

Physics 1D03 - Lecture 8 1

Newton’s Laws (IV)Newton’s Laws (IV)

• Blocks, ramps, pulleys and other problems


To be handed in for marks on Friday !!!

A block of mass m=5kg is pulled with a force A block of mass m=5kg is pulled with a force FFAA = 10N= 10N at at

an angle an angle θθ=45=45oo to the horizontal, find the acceleration. to the horizontal, find the acceleration. Friction is given by Friction is given by μμkk=0.1=0.1. .

m

θ

FA

Include you NAME and Student #


Two blocks connected by a rope are being pulled by a horizontal force FA. Given that F=60 N, m1=12kg and m2=18kg, and that μk=0.1, find the tension in the rope between them and the acceleration of the system.

m1m2 FA

T


Elevator go up, elevator go down

• A person of mass 70kg is standing on a scale in an elevator at rest. What is her weight ?

• What is her weight when the elevator is accelerating up at 5m/s2 ???

• What is her weight when the elevator is accelerating down at 5m/s2 ???


Pulleys

• To solve pulley problems, we assume that:

1) the pulley is frictionless

2) the pulley is massless

• Hence, the force of tension on both sides of the pulley is the same


Example• Find the acceleration of a system of two masses

m=5kg and M=10kg. The angle θ=30o. No friction!• Also, find the tension, T, in the string.

M

m

There are two ways of solving the problem !


Kinematics in Two DimensionsKinematics in Two Dimensions

• Position, velocity, acceleration vectors

• Constant acceleration in 2-D

• Free fall in 2-D


The Position vector points from the origin to the particle.

r

The components of are the coordinates (x,y) of the particle:

For a moving particle, , x(t), y(t) are functions of time.

ji yxr

)(tr

r

x

y

r

(x,y)

path

xi

yj


ji yxr

(i, j are unit vectors)

ji

ji

yx vv

dt

dy

dt

dxdt

rdv

the unit vectors are constants

We get velocity components by differentiation:

Components: Each vector relation implies 2 separate relations for the 2 Cartesian components.


Constant Acceleration + Projectile Motion

a

If is constant (magnitude and direction), then:

22

1 t)(

)(

tavtr

tavtv

o

o

Where is the initial value at t = 0.ov

In 2-D, each vector equation is equivalent to a pair of component equations:

22

1

22

1

t)(

t)(

tavty

tavtx

yoy

xox

Example: [down] m/s 8.9 :fall Free 2ga


Shooting the Gorilla

Tarzan has a new slingshot. George the gorilla hangs from a tree, and bets that Tarzan can’t hit him. Tarzan aims at George, and is sorry that he didn’t pay more attention in physics class. Where should he aim?


Example Problem

A stone is thrown upwards from the top of a 45.0 m high building with a 30º angle above the horizontal. If the initial velocity of the stone is 20.0 m/s, how long is the stone in the air, and how far from the base of the building does it land ?

physics 1d03 - lecture 81 newton’s laws (iv) blocks, ramps, pulleys and other problems

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