REVIEW FOR MID TERM 1

SI CGS BE

Length Meter (m) Centimeter (cm)

Foot (ft)

Mass Kilogram (kg)

Gram (g) Slug (sl)

Time Second (s) Second (s) Second (s)

English S.I.

• 1 inch = 2.540 cm (centimeter = 1/100 meter)

• 1mile = 1.609 km (kilometer= 1000 meters)

• 1 pound = 454 g (gram)

• 1.06 quart = 1 L (litre)

Components Of Vectors

A = Ax + Ay

Using Components To Add Vectors

Cx = Ax + Bx

Cy = Ay + By

Vav,x = (x2-x1)/(t2-t1) = Δx/Δt SI unit: m/s

Average Accelerationaav,x = (v2x – v1x) / (t2 - t1) = Δvx / Δt

SI unit: m/s2

Instantaneous Accelerationax = lim (Δvx/Δt) Δt 0SI unit: m/s2

Cars Accelerating or Decelerating

Constant-Acceleration Equations of Motion

Variables Related Equation

Velocity, time, acceleration

vx = v0x + axt

Position, time, acceleration

x = x0 + v0xt + (½ )axt2

Velocity, position, acceleration

vx2 = v0x

2 + 2ax(x – x0) = v0x2 + 2axx

Constant-Acceleration Equations of Motion in Two-Dimensions

vx = v0x + axt vy = v0y + ayt

x = x0 + v0xt + (½ )axt2 y = y0 + v0yt + (½ )ayt2

vx2 = v0x

2 + 2ax(x – x0) vy2 = v0y

2 + 2ay(y – y0)

Equations of Motion for projectileax = 0m/s2 ay = -9.81m/s2

vx = v0x + axt vy = v0y + ayt

x = x0 + v0xt + (½ )axt2 y = y0 + v0yt + (½ )ayt2

vy2 = v0y

2 + 2ay(y – y0)

Determination of key itemsfor projectiles

• x = (vocos o)t

= tan-1(vy/vx)

• y = (vosin o)t - ½gt2

• vx = vocoso

• vy = vosino- gt

R = F1 + F2 + F3 + ……..= Σ F, (resultant, and vector sum, of forces)

Rx = Σ Fx , Ry = Σ Fy

(components of vector sum of forces)

Once we have the components Rx and Ry, we can find the magnitude and direction of the vector R.

Newton’s First Law – Figure 4.7

•“Objects at rest tend to stay at rest and objects in motion tend to stay in motion in a straight line unless it is forced to change that state by forces acting on it”

Newton’s Second Law of Motion (Vector Form)

The vector sum (resultant) of all the forces acting on an object equals the object’s mass times its acceleration :

ΣF = ma

The acceleration a has the same direction as the resultant force ΣF.

Newton’s Second Law of Motion (Vector Form)

The vector sum (resultant) of all the forces acting on an object equals the object’s mass times its acceleration :

ΣF = ma

The acceleration a has the same direction as the resultant force ΣF.

Forces are the origin of motionForces Acceleration a = F/m

Velocityv= v0 + at

Positionx = x0 + v0t + ½ at2

x

y

x positivey positive

x negativey positive

x

y

x

y

x negativey negative

x

y

x positivey negative

x

y

??????

x positivey positive

Drawing a FBD of forces on an object (on, not by)

1. Choose the object to analyze. Draw it as a dot.2. What forces physically touch this object?

This object, not some other3. What “action at a distance” forces act on the object?

Gravity is the only one for this PHYS2053

4. Draw these forces as arrows with tails at the dot (object).5. Forces only! No accelerations, velocities, …

Get components of Newton’s 2nd Law

Choose a convenient xy coordinate systemFind the x and y components of each force in the FBDAdd the x and y components separately

In a rescue, the 70.0  police officer is suspended by two cables, as shown in the figure below Find the tension in the cables.

w

T2T1

T2 cos480

T2 sin480

T1 sin350

T1 cos350

35o48o

x

y