Chapter 1: Kinematics and Dynamics Flashcards
(26 cards)
Unit of mass in the imperial system? Therefore, imperial unit of force? Metric unit of force?
Slug. (slug * foot) /(second^2)
Newton: kg*m/s^2
Simplifications for: sin0? cos0? tan0? sin30? cos30? tan30? sin45? cos45? tan45? sin60? cos60? tan60? sin90? cos90? tan90?
0, 1, 0 1/2, (sqrt3)/2, (sqrt3)/3 (sqrt2)/2, (sqrt2)/2, 1 (sqrt3)/2, 1/2, sqrt3 1, 0, infinity
How to find the resultant of multiple vectors?
- break into X and Y components
- add up each components to get resultant X and Y
- use pythagorean theorem
- find direction by using theta = inverse tan (opp/adj)
What happens when you multiply a scalar by a vector?
Vector increases in magnitude and either points in the same direction or in the exact opposite direction (if the scalar is negative)
How do you multiply two vectors to get a scalar quantity, like work (force times displacement)? (dot product)
A . B = |A| |B| cos theta
theta is the angle between the two vectors (90 if one is just an x quantity and the other is just a y)
How do you multiply two vectors to get a third vector, like torque? (cross product)
A x B = |A| |B| sin theta
use right hand rule to determine direction of resultant: thumb is A, fingers are B, palm points in direction of C
Difference between instantaneous velocity and instantaneous speed?
Between average velocity and average speed?
Same magnitude.
Different, as speed takes distance traveled into account whereas velocity accounts for displacement
Formula for gravitational force?
F = Gm1m2/r^2,
where G is the universal gravitational constant (6.67E-11), m1 and m2 are the two object masses and r is the radius between them. Simplify G to 20/3E-11
Equation for static friction? (resting object)
0 less than equal to (F_s) less than equal to (U_s *N)
Where F_s is static friction, U_s is the coefficient of static friction and N is the normal force (force pushing up from ground). Can be anywhere in that range from zero to right side of equation
Equation for kinetic friction?
F_k = U_k*N
Where U_k is the coefficient of kinetic friction and N is the normal force. U_k is always smaller than U_s
Force of gravity equation? (weight)
F_g = mg, where m is mass in kg and g is acceleration due to gravity = 9.8m/s^2 (round to 10)
Acceleration formula?
change in velocity over change in time
Newton’s first law? Equation?
A body at either at rest or in motion with constant velocity will remain that way unless a net force acts on it. F_net = ma = 0
Newton’s second law? equation?
An object with mass m will accelerate when the vector sum of the forces results in some nonzero resultant force vector. F_net = ma
Newton’s third law? Equation?
To every action there is an opposed but equal reaction.
F_ab = -F_ba
What constitutes linear motion?
When an object’s velocity and acceleration are in the same direction
Equations which describe linear motion? (4 of these badboys, know them for all the kinematics problems)
- V = V_o + at
- x = V_o*t + a(t^2)/2
- v^2 = V_o^2 + 2ax
- x = v!t
where x (or y), v and a are the displacement, velocity and acceleration vectors, V_o is initial velocity, v! is average velocity (really has a line over it not an !), and t is time
Conditions for a free-fall problem?
No air-resistance, acceleration is 9.8m/s^2, and no terminal velocity
What constitutes projectile motion?
Motion that follows a path along 2 dimensions. Velocity and acceleration are in the two directions (usually horizontal and vertical) and must be separated from one another. Horizontal velocity typically remains constant, while vertical velocity is accelerated downward due to gravity
How to find vertical and horizontal velocity of an object launched at an angle (ex 37 degrees at 50m/s)
V_oy = 50sin37 = 50*0.6 = 30 V_ox = 50cos37 = 50*0.8 = 40
How do you divide inclined plane questions into horizontal and vertical force vectors due to gravity?
F_gparallel = mg(sin theta) F_gperpendicular = mg(cos theta)
In uniform circular motion, where is the instantaneous velocity? Where does centripetal force point?
Tangent to the circular path. Towards the center of the circle
Equation that describes circular motion?
F_c = m(v^2)/r
where F_c is centripedal force, m is the mass, v is the speed and r is the radius
In rotational equilibrium, what is the lever arm?
The distance between the applied force and the fulcrum (pivot point)
