Systems of Particles & Accelerations

Question 1

Describe in terms of particles the force in an object.

Answer 1

Fi + sum of j =/ i of Fij = mi*ai, where Fi is the external force on a particle. Then add a sum over all particles (sum sign with i below it for each term. Sum of j =/ i of Fij goes to zero as for every ji term there is an ij term. This leaves F = sum of all i of mi * ai.

Question 2

How do you work out the position of the centre of mass (x-component)?

Answer 2

xcm = int(x dm) / int(dm), where dm is an infinitesimal element of mass.
An example is int(dm) = ϱ dx, where ϱ is the density.

Question 3

How would you work out the acceleration of a block on a slope if the forces are not balanced?

Answer 3

• Write equations for the force pair (weight component and normal reaction and frictonal force and weight component)
• Use Fk = µK*N
• Rearrange for acceleration

Question 4

What do you do in a problem where a block is on a wedge but the wedge can also move?

Answer 4

To apply F = ma we must add the acceleration of the wedge so we are judging relative to an inertial frame (a = a1 + a2)

Question 5

What does the word “light” mean in physics? (e.g. a light pulley)

Answer 5

Zero mass, no force needed to accelerate it.

Question 6

What is meant by elastic?

Answer 6

Conserves kinetic energy (inelastic loses energy to heat and sound etc)

Question 7

How do you work out the acceleration of a mass attached to pulleys?

Answer 7

Use F = mg and take away the tension in the rope, and make it equal to ma (mg - T = ma).

Question 8

What are the 3 main constant acceleration equations?

Answer 8

• v = u + at
• s = ut + 1/2 * at^2
• v^2 = u^2 + 2as

Question 9

How do you derive the constant acceleration equations?

Answer 9

• Rearrange dv/dt = a to dv = a dt, then integrate
• rearrange v = dx/dt to v dt = dx, substitute what you got for the last equation for v and integrate again
• rearrange first equation for t and substitute this in and rearrange

Question 10

What do you do for time dependant acceleration?

Answer 10

You need to leave a(t) inside the integral as it is not constant.

Question 11

What do you do for position dependant acceleration?

Answer 11

• Write a(x) as v dv/dx
• Can write this as v dv = a dx
• Integrate both sides

Question 12

What do you do for velocity-dependant acceleration?

Answer 12

• dv/dt = a(v)

- Rearrange to dv/a(v) = dt and integrate both sides