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union e particuculas entre si
AQA Mechanics 1 Newton’s Laws of motion Section 2: Connected particles Solutions to Exercise 1.
a
T T
3 kg
a
9 kg 3g 9g
T 3g 3a 9g T 9a 6g 12a
Considering 3 kg mass: Considering 9 kg mass: Adding:
(1) (2)
a 21 9.8 4.9 The acceleration of the system is 4.9 ms-2. (1) gives T 3g 3a
3( 9.8 4.9) 44.1 The tension in the string is 44.1 N. 2. Resistance experienced by engine 60000 80 4800000 Resistance experienced by truck 12000 50 600000 Train is travelling at constant speed, so acceleration is zero.
R1
R2 12000 kg
T
T
60000 kg
X
4800000
600000
60000g
12000g Considering whole system:
X 4800000 600000 0 X 5400000
The driving force of the engine = 5400 kN. Considering truck:
T 1 8 g 8a (1) Considering 5 kg mass: T2 5 g 5a T2 5 g 5a (2) Considering the 10 kg mass: (3) T 1 T 2 10a Substituting (1) and (2) into (3): 8 g 8a (5 g 5 a ) 10a 3g 23a 3 9.8 1.28 23 The acceleration of the system is 1.28 ms-2 (3 s.f.)
a
Substituting into (1):
68.2 Substituting into (2):
3 9.8 23
T 1 8 9.8 8
3 9.8 23
T 2 5 9.8 5 55.4
The tensions in the strings are 68.2 N and 55.4 N (3 s.f.)
Considering particle on table: T ma Considering hanging particle: mg T ma Adding: mg 2ma
a 4.9, u 0, t 0.5
a 21 g 4.9
s ut 21 at 2 0 21 4.9 0.5 2 0.6125 Distance travelled = 0.6125 m
v u at 0 4.9 0.5 2.45 Speed = 2.45 ms-1.
7.
R 6g 0 R 6 9.8 58.8 Friction is limiting so F R F 0.4 58.8 23.52 Horizontally for the box: T F 6a T 23.52 6a (1) 3g T 3a For 3 kg mass: (2) Vertically for the box: