Mechanics 2: Motion, Kinematics, Dynamics, and Newton's Laws

Flashcards covering kinematic equations, projectile motion, graphical analysis of motion, Newton's three laws, and motion through fluids as derived from the physics lecture transcript.

What is the definition of velocity according to the transcript?

Velocity is the rate of change of displacement ($v = \frac{\Delta s}{\Delta t}$).

What is the definition of acceleration?

Acceleration is the rate of change of velocity ($a = \frac{\Delta v}{\Delta t}$).

State the SUVAT equation that relates final velocity, initial velocity, acceleration, and time.

$$v = u + at$$

State the SUVAT equation used to find displacement ($s$) without using final velocity ($v$).

$$s = ut + \frac{1}{2}at^2$$

State the SUVAT equation for $v^2$.

$$v^2 = u^2 + 2as$$

What value for acceleration due to gravity ($g$) is used in the notes?

$$g = 9.81\,ms^{-2}$$

What is terminal speed (terminal velocity)?

The maximum speed reached by an object travelling through a fluid, when the driving force equals the drag force and acceleration is zero.

According to the independence of motion in projectiles, how is horizontal motion treated?

There is no horizontal acceleration ($a_H = 0$), so the constant velocity equation $s = vt$ is used, and air resistance is ignored.

What is the physical significance of the gradient of a displacement-time graph?

The gradient represents the velocity.

What is the physical significance of the area under a velocity-time graph?

The area represents the displacement.

What does the gradient of a velocity-time graph represent?

The gradient represents the acceleration.

State Newton’s First Law of Motion.

A body at rest will remain at rest ($v = 0$) or maintain a constant velocity unless acted upon by a resultant force.

State Newton’s Second Law for a constant mass.

Resultant force is equal to the product of mass and acceleration ($F_R = \Sigma F = ma$).

State the original version of Newton’s Second Law involving momentum.

Resultant force is equal to the rate of change of momentum ($F_R = \frac{\Delta mv}{\Delta t}$).

State Newton’s Third Law of Motion.

If body A exerts a force on body B, then body B exerts an equal and opposite force (of the same type) on body A.

What are the four key characteristics of a Newton’s third law pair of forces?

1. They act on two different bodies. 2. They are equal in magnitude. 3. They are opposite in direction. 4. They must be the same type of force.

Which force acts vertically upwards on bodies in fluids and is equal to the weight of the displaced fluid?

Buoyant upthrust ($F_B = \rho gV$).

In the context of friction, what is the difference between 'smooth' and 'rough' surfaces?

'Smooth' means the coefficient of friction ($\mu$) is 0; 'rough' means $\mu > 0$.

What is the direction of Normal Contact Force relative to the contact surface?

It always acts at $90^{\circ}$ ('normal') to the contact surface.

How does air resistance (drag) change as the speed of an object increases?

Air resistance increases with speed ($F_D \propto v^2$).

What happens to the vertical velocity of a projectile at the top of its flight arc?

The vertical velocity is momentarily zero ($v_V = 0$).

How is the range of a projectile defined?

The range is the distance travelled in the horizontal direction.

Describe the initial acceleration of a skydiver in freefall at the moment they jump.

The velocity is initially zero, so air resistance is zero; the resultant force equals the skydiver's weight, and acceleration equals $g$ ($9.81\,ms^{-2}$).

What is the effect of opening a parachute on a skydiver's motion?

It rapidly increases surface area and air resistance, making air resistance greater than weight, resulting in a upward resultant force and negative acceleration (deceleration).

On a displacement-time graph, what does a curved line indicate?

A curved line indicates changing velocity, which is acceleration.