Workseet 2FA Marking scheme

1    a    θ =  ´ 2π =  » 0.52 rad                                                                                                [1]

b    θ =  ´ 2π » 3.7 rad                                                                                                          [1]

c    θ =  ´ 2π » 8.7 ´ 10⁻⁴ rad                                                                                               [1]

2    a    θ =  ´ 360 = 57.3° » 57°                                                                                                   [1]

b    θ =  ´ 360 » 230°                                                                                                            [1]

c    θ =  ´ 360 » 8.6°                                                                                                           [1]

3    a    88 days is equivalent to 2π radians.
θ =  ´ 2π = π rad                                                                                                              [1]

b    θ =  ´ 2π » 0.071 rad (4.1°)                                                                                              [1]

4    a    w =  =                                                                                                                   [1]
w = 7.5 ´ 10⁵ rad s⁻¹                                                                                                              [1]

b    a =                                                                                                                                  [1]
a =                                                                                                                            [1]
a = 1.125 m s^–2 » 1.1 m s⁻²                                                                                                     [1]

c    F = ma = 80 ´ 1.125                                                                                                              [1]
F = 90 N                                                                                                                               [1]

5.   a    i     Time =  = 0.82 s                                                                                                        [1]

ii    Distance = circumference of circle = 2π ´ 0.80 = 5.03 m » 5.0 m                                        [1]

iii   speed =  =                                                                                                 [1]
speed, v = 6.13 m s⁻¹ » 6.1 m s⁻¹                                                                                       [1]

iv   a =                                                                                                                            [1]
a =                                                                                                                        [1]
a = 47 m s^–2                                                                                                                     [1]

v    F = ma = 0.090 ´ 47                                                                                                        [1]
F » 4.2 N                                                                                                                        [1]

6    net force =

net force =  = 2.4 N                                                                                                 [2]

weight W of stone = mg = 0.120 ´ 9.81 = 1.18 N » 1.2 N                                                               [1]

At the top: W + T_B = 2.4 so T_B = 2.4 - 1.2 = 1.2 N                                                                   [1]

At the bottom: T_A - W = 2.4 so T_A = 2.4 + 1.2 = 3.6 N                                                              [1]

ratio =  =  = 3.0                                                                                                               [1]