Practice Sheet 8 - Sample Solutions¶

In [1]:

class Particle(object):
    
    def __init__(self, mass, x, y, z, vx, vy, vz):
        self.mass = mass
        self.x = x
        self.y = y
        self.z = z
        self.vx = vx
        self.vy = vy
        self.vz = vz
        
    def kinetic_energy(self):
        return 0.5 * self.mass * (self.vx ** 2 + self.vy ** 2 + self.vz ** 2)
    
    def separation(self, other):
        return np.sqrt((self.x - other.x) ** 2 + (self.y - other.y) ** 2 + (self.z - other.z) ** 2)
    
    def move(self, dt):
        self.x += dt * self.vx
        self.y += dt * self.vy
        self.z += dt * self.vz

In [2]:

p1 = Particle(1., 5.5, 4.4, 3.4, 3.4, 4.4, 7.7)
p1.kinetic_energy()

Out[2]:

45.105000000000004

In [3]:

p2 = Particle(0.2, 3.3, 4.1, 3.1, -2.2, 4.4, -5.4)
p1.separation(p2)

Out[3]:

2.2405356502408083

In [4]:

p2.separation(p1)

Out[4]:

2.2405356502408083

In [5]:

p1.move(1.)
print p1.x, p1.y, p1.z

8.9 8.8 11.1

In [6]:

for i in range(10):
    p1.move(0.1)
    print p1.x, p1.y, p1.z

9.24 9.24 11.87
9.58 9.68 12.64
9.92 10.12 13.41
10.26 10.56 14.18
10.6 11.0 14.95
10.94 11.44 15.72
11.28 11.88 16.49
11.62 12.32 17.26
11.96 12.76 18.03
12.3 13.2 18.8

In [7]:

class ChargedParticle(Particle):
    def __init__(self, mass, x, y, z, vx, vy, vz, charge):
        self.charge = charge
        Particle.__init__(self, mass, x, y, z, vx, vy, vz)  # avoids having to re-define all the attributes

In [8]:

p3 = ChargedParticle(4., 2.2, 3.2, 4.3, 6.6, -2.3, 2.2, -1)

In [9]:

p3.separation(p1)

Out[9]:

20.304186760370378

In [10]:

p3.charge

Out[10]:

-1