Friction
When do I use μs and when do I use μk?
μs: Stationary objects
μk: Objects in motion
Where does the Normal Force point towards?
Perpendicular to the surface an object is resting on.
What is the unit for Work?
Joules [J]
How can we define Momentum and Impulse? (formula)
Momentum: m*v
Impulse: F*t
True or False.
In Direct Central Impact, the initial and final velocity vectors of both objects are along the line of impact.
True!
Direct Central Impact is one-dimensional motion (all movement and forces happen along a single straight line).
Where does the Friction force vector point towards?
Opposite to the direction of motion.
What is represented on a Free Body Diagram?
Forces acting on the object.
When talking about Work, what is T?
Kinetic Energy.
T = 1/2 mv2
What is the formula for the Principle of Impulse and Momentum?
mv1 + sum (int t1->t2 F dt) = mv2
Define "e" (formula)
Coefficient of restitution:
e = (v'B - v'A) / (vA - vB)
What is this called and what are it's units?
μ
Coefficient of Friction. Can be Static (μs) or Kinetic (μk).
It is unitless! Ff = N*μ
True or False
I can't use the conventional coordinate system (↑+y →+x) in this free body diagram.
False. I can use it but it may be more convenient to use an inclined coordinate system.
What is the Work done by a spring?
Ws = 1/2 kx2
What formula can I use when there is Conservation of Linear Momentum?
sum mi(vi)1 = sum mi(vi)2
Which is the Line of impact and which is the Plane of contact for both of these scenarios?
Line of impact: Passes through contact point and is perpendicular to plane of contact.
Plane of contact: Geometric surface tangent to the objects at the impact point.
A 10 kg block with a kinetic friction coefficient of 0.3 is moving to the right on a flat surface, using g = 9.8 m/s² and +x to the right, how much is the Friction Force, what units does it have, and which direction is it pointing towards?
-29.4 Newtons (or 29.4N in -x direction)
A 10 kg box is pulled right with a 50 N force across a floor with μs = 0.10 and μk = 0.20. What is the resulting acceleration?
3.04 m/s²
If I triple my velocity, what happens to kinetic energy?
Kinetic energy increases by a factor of 32.
When do we have conservation of linear momentum?
- The sum of forces acting on the system is zero.
- The resultant force in a given direction is zero.
Give the definition and formula for each of these special cases of direct central impact:
- Perfectly Plastic Impact (hint: e=0)
- Perfectly Elastic Impact (hint: e=1)
- Perfectly Plastic Impact: Total momentum of the particle is conserved.
v'B = v'A = v'
mAvA + mBvB = (mA + mB)v'
- Perfectly Elastic Impact: Total energy and total momentum of the particles are conserved.
v'B - v'A = vA - vB
Define μs and μk
μs: The resistance that must be overcome to start moving a stationary object
μk: The resistance that acts on an object while it is actively sliding across a surface.
If my coordinate system is inclined theta degrees, which force is not doing any Work? Why?
Normal Force.
Forces perpendicular to the distance do NOT do Work.
W = F*dcos(β), with β being the angle between the distance and the force we are analyzing.
-> cos(β) = cos(90) = 0
W = F*d*0 = 0
When do I use:
T1 + U1->2 = T2
and when do I use:
T1 + V1 = T2 + V2 ?
When a Non-Conservative Force is Being Applied:
T1 + U1->2 = T2
ONLY when a Conservative Force is being applied:
T1 + V1 = T2 + V2 ?
True or false:
Principle of Impulse and Momentum equation is a scalar equation. Justify.
False! It is a vector equation that can be broken down into scalar components (x, y, z components).
What does this mean?
It accounts for magnitude AND direction while scalar components only account for magnitude.
What is conserved in Oblique Central Impact?
Tangential momentum is conserved separately for each particle in Oblique Central Impact because there are no impulses exchanged in the t-direction.
vt = v't