a level : circular motion_answer
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worksheetTRANSCRIPT
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AS and A Level Physics Original material Cambridge University Press 2010 1
18 Marking scheme: Worksheet (A2)
1 a = 36030 2 = 6
0.52 rad [1]
b = 360210 2 3.7 rad [1]
c = 360
05.0 2 8.7 104 rad [1]
2 a = 20.1 360 = 57.3 57 [1]
b = 20.4 360 230 [1]
c = 215.0 360 8.6 [1]
3 a 88 days is equivalent to 2 radians.
= 8844 2 = rad [1]
b = 881 2 0.071 rad (4.1) [1]
4 a Friction between the tyres and the road. [1] b Gravitational force acting on the planet due to the Sun. [1] c Electrical force acting on the electron due to the positive nucleus. [1] d The (inward) contact force between the clothes and the rotating drum. [1]
5 a = rv
= 20000150
[1]
= 7.5 105 rad s1 [1] b a =
rv2 [1]
a = 000 20
1502 [1]
a = 1.125 m s2 1.1 m s2 [1] c F = ma = 80 1.125 [1]
F = 90 N [1] 6 a i Time =
102.8 = 0.82 s [1]
ii Distance = circumference of circle = 2 0.80 = 5.03 m 5.0 m [1] iii speed =
timedistance =
82.003.5 [1]
speed, v = 6.13 m s1 6.1 m s1 [1] iv a =
rv 2 [1]
a = 80.0
13.6 2 [1]
a = 47 m s2 [1]
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18 Marking scheme: Worksheet (A2)
AS and A Level Physics Original material Cambridge University Press 2010 2
v F = ma = 0.090 47 [1] F 4.2 N [1]
b The tension in the string. [1] c The stone describes a circle, therefore the angle between the velocity and the acceleration
(or centripetal force) must be 90. [1]
7 a i speed = time
distance
speed v = 1.6
0.1222 =T
r [1]
v = 0.471 m s1 0.47 m s1 [1] ii
rmvmaF
2
== [1]
12.0471.0300.0 2=F [1]
frictional force 0.55 N [1] b Frictional force = 0.7mg [1]
rmvmg
2
7.0 = [1] 12.081.97.07.0 == grv [1]
speed = 0.908 m s1 0.91 m s1 [1] 8 a Kinetic energy at B = loss of gravitational potential energy from A to B
21 mv2 = mgh or v = gh2 [1] v = 2.581.92 =10.1 m s1 10 m s1 [1]
b i a = r
v 2 [1]
a = 16
1.10 2 [1]
a = 6.38 m s2 6.4 m s2 [1] ii Net force = ma
R mg = ma [1] R = mg + ma = m(a + g) = 70(6.38 + 9.81) [1] R 1.1 103 N [1]
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18 Marking scheme: Worksheet (A2)
AS and A Level Physics Original material Cambridge University Press 2010 3
9 a R cos 20 = W = 840 9.8 [1]
R = 20 cos
8.9840 = 8760 N [1]
b R sin 20 = centripetal force = r
mv2 [1]
r = R
mv2 [1]
r =
20sin 876032840 2 [1]
r = 287 m 290 m [1]
10 net force = r
mv2
net force = 80.0
0.4120.0 2 = 2.4 N [2] weight W of stone = mg = 0.120 9.81 = 1.18 N 1.2 N [1] At the top: W + TB = 2.4 so TB = 2.4 1.2 = 1.2 N [1] At the bottom: TA W = 2.4 so TA = 2.4 + 1.2 = 3.6 N [1] ratio =
B
A
TT
= 2.16.3 = 3.0 [1]