Dynamics Midterm 1 SA

Define position and list its unit.

The location of a particle in space relative to a reference point.

meters

Define displacement and list its unit.

The change in position of a particle.

meters

Define velocity and list its unit.

ds/dt

m/s

Define average velocity and list its unit.

Change in displacement divided by the change in time.

m/s

Define speed and list its unit.

The magnitude of velocity (always positive).

m/s

Define average speed and list its unit.

The total distance divided by the change time.

m/s

Define acceleration and list its unit.

dv/dt

m/s²

Define average acceleration and list its unit.

The change in velocity divided by the change in time.

m/s², ft/s²

What do positive and negative signs indicate for velocity?

Positive and negative signs indicate velocities direction.

What do positive and negative signs indicate for acceleration?

Positive acceleration indicates an increase in acceleration, while negative acceleration indicates deceleration.

Describe the mathematical relationships between position, velocity, acceleration, and time.

v = ds/dt

a = dv/dt

ads = vdv

What do the slopes represent in s-t and v-t graphs?

In s-t graphs, the slope represents velocity; in v-t graphs, the slope represents acceleration.

What do the areas represent in a-t, v-t, and a-s graphs?

In a-t graphs, the area represents change in velocity; in v-t graphs, the area represents change in displacement; in a-s graphs, the area represents ½(v₂²-v₁²).

How do you describe the motion of a particle along a known path (where s is a function of time) in x, y, z coordinates?

r = xi + yj + zk
v = x’i + y’j + z’k
a = x”i + y”j +z”k

What is projectile motion?

Free-flight motion of a projectile that follows a parabolic path.

How do you determine normal and tangential axes for a particle on a curvilinear path?

at is tangent of the curve. an is perpendicular to at in the concave direction.

How do you represent velocity and acceleration using the n-t axes?

v = v * u_t
a = v’ * u_t + v²/rho * u_n

What are the physical interpretations of tangential acceleration (at) and normal acceleration (an)?

at is rate of change of speed. an is rate of change of direction.

What are the limitations of the equation F=ma?

When a particle travels with light speed, or the particle is the size of an atom.

How do you calculate the gravitational constant using F=Gm1m2/r²?

G = F r² / (m₁ m₂)

What is an inertial reference frame, and why is it needed?

A reference frame that is fixed or has a constant velocity. It provides a consistent basis for calculations.

Differentiate between external forces and internal forces in a system of particles.

External forces act on a system from outside like gravity, while internal forces are interactions between particles within the system.

Define work and its units.

u_1-2 = int (Fdr)

Joules (J) = N⋅m

Define energy and its units.

The capacity to do work.

Joules (J) = N⋅m (same units as work)

Define power and its units.

The rate of change of work.

Watt (W), J/s = N⋅m/s

Define power efficiency and its units.

P_out / P_in

Since it's a ratio it's unitless.

What is a conservative force?

When the work of a force is only dependent on a force’s initial and final positions

What do positive work and negative work signify?

Positive work: force is in the same direction as its displacement.
Negative work: force is in the opposite direction of its displacement.

Explain the principle of work and energy.

The net work done on an object is equal to its change in kinetic energy.

Describe the principle of conservation of energy.

The total energy of a closed system remains constant over time.

Define potential energy.

Amount of work a conservative force must do from a given position to datum.

How do you determine whether a force is conservative?

If the work is dependent on the initial and final positions.