Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova

Lecture 10

A physics professor did daredevil stunts in his spare time. His last stunt was an attempt to jump across a river on a motorcycle. The takeoff ramp was inclined at 53.00, the river was 40.0 m wide, and the far bank was 15.0 m lower than the top of the ramp. The river itself was 100 m below the ramp. You can ignore air resistance. a) What should his speed have been at the top of the ramp to have just made it to the edge of the far bank? b) If his speed was only half the value found in (a), where did he land?

A faulty model rocket moves in the xy-plane (the positive y-

direction is vertically upward). The rocket’s acceleration has

components ax(t)=t2 and ay(t)=-t, where =2.50 m/s4, =9.00

m/s2, and =1.40 m/s3. At t=0 the rocket is at the origin and has

velocity with and

a) Calculate the velocity and position vectors as functions of time.

b) What is the maximum height reached by the rocket?

c) What is the horizontal displacement of the rocket when it

returns to y=0?

jvivvyx

000 smv

x/00.10 ./00.70 smv y

An object’s acceleration is given by

If the object starts at t=0 at the origin with an initial velocity of magnitude Vi directed at θ above the x axis, what are its velocity and position at any time?

jtita 2

Dynamics

Connection between force and motion

The concept of force gives us a quantitative

description of the interaction between two bodies or between a body and its environment

Newton’s Laws

1st Law: A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration2nd Law: The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object.3rd Law: For every action there is an equal, but opposite reaction

2nd Law

From experiments we know:1.Force is a vector2.The direction of acceleration vector is the

same as the direction of the force vector3.The magnitude of the force and

acceleration are related by a constant which depends on number of blocks involved.

amF

Newton’s second law

The vector acceleration of an object is in the same direction as the vector force applied to the object and the magnitudes are related by a constant called the mass of the object.

Gravitational force gmF

Force exerted by a spring:Hooke’s law: If spring is stretched or compressed by some small amount it exerted a force which is linearly proportional to the amount of stretching or compressing. The constant of proportionality is called the spring constant

xxkFspring ,

-is deviation from the natural length

Normal force

The force resisting the pull of the spring – frictionThere is some maximum value the friction force can achieve, and once we apply a force greater than this maximum there is a net force on the object, so it accelerates.

The maximum of the force of friction varied linearly with the amount that the block pushes on the table.

NFfriction

- coefficient of friction, is the vertical force exerted by

the block on the table N

The friction force only exists when there is another force trying to move an object

A Recipe for Solving Problems1. Sketch Isolate the body (only external forces but not forces

that one part of the object exert on another part)

2. Write down 2nd Newton’s law

amF

Choose a coordinate system Write 2nd Newton’s law in component form:

yyxx

yxyx

maFmaF

jmaimajFiFF

,

3. Solve for acceleration

Have a great day!

Reading: Chapter 5,6Hw: Chapter 6 problems and exercises