In-Tutorial Tutorial Assignment 1
APM2EA1
Due: 13 February 2017, 15H25 (to be submitted with At-Home Tutorial
Assignment 1)
Tutorial Assignment 1 is worth 10 Marks
Note. Bar notation will be used to represent vectors, for instance, r.
Problem 1:
A particle is at a point A in a right-handed Cartesian reference system with
origin O = (0, 0, 0) at time t0 = 0 s. The particle experiences a uniform
velocity and at time t1 is at a point B. At time t1 , the particle experiences a
uniform velocity and at time t2 is at a point C. Let r1 := OA and r2 := OB.
Suppose that the particle travels a distance d in each of the time intervals
∆t2 := t2 − t1 and ∆t1 := t1 − t0 . With appropriate reasoning, determine
whether or not the system is in equilibrium and if so, whether or not the
system is in static equilibrium for the following scenarios:
1. A 6= O and r̂1 6= r̂2 .
2. A 6= O, r̂1 = r̂2 and ∆t2 6= ∆t1 .
3. A 6= O, r̂1 = r̂2 and ∆t2 = ∆t1 .
4. A 6= O, n̂1 = nˆ2 and ∆t2 = ∆t1 , where
n̂1 =
AB
d
and n̂2 =
5. A = O and r̂1 6= r̂2 .
1
BC
.
d
6. A = O and r̂1 = r̂2 .
Problem 2:
Use the definition of equilibrium to show that N1 is a special case of N2.
Furthermore, show that static equilibrium is a particular case of equilibrium.
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