physics momentum 10 points

用戶129495

2009-04-29 2:20 am

A car , which is travelling with a speed of 80 km/h is colliding with a lorry which is travelling in the opposite direction . They stick together and come to rest after the collision . The impact time is 0.3 s . Suppose that the total mass of the car and its driver is 1000 kg and that of the lorry is 5000kg

a) find the speed of the lorry before collision
b) suppose the masses of the two drivers are both 70kg
find the impact force acting on the car driver , F
Also find the average impact force acting on the lorry driver , d
c)verify that the ratio of the average forces acting on the drivers satisties the followin relation , from the result of part b

F/d=(1/total mass of car and car driver )/(1/total mass of lorry and its driver)

d)prove the ratio found in part c is generally true.In other words , the ratio found in part c is independent of the speeds of the venhicles before the collision

e) from the result of part c , compare the injuries got by the drivers during car accidents

回答 (1)

天同

2009-04-29 3:53 am

✔ 最佳答案

(a) using conservation of momentum
1000 x (80/3.6) + 5000u = 0
where u is the speed of the lorry before collision
hence, u = - 4.44 m/s or -16 km/h
(b) since force on driver x impact time = change of momentum of driver
F x 0.3 = 70 x 80/3.6
i.e. F = 5185 N
d x 0.3 = 70 x 4.44
i.e. d = 1036 N
(c) F/d = 5185/1036 = 5
(1/total mass of car and car driver )/(1/total mass of lorry and its driver)
= (1/1000)/(1/5000) = 5000/1000 = 5
Hence, they are equal.
(d) since F. t = mu and d.t = m.U
where t is the impact time
m is the mass of the driver
u and U are the velocities of the car and lorry before collision
hence, F/d = u/U
But from conservation of momentum
(Mc).u = (Ml).U
where Mc and Ml are the masses of the car and lorry respectively
i.e. u/U = Ml/Mc = (1/Mc)/(1/Ml)
thus, F/d = (1/Mc)/(1/Ml)
(e) The force acted on the car driver is 5 times that acted on the lorry driver. Hence, the car driver would have more serious injury than the lorry driver. This is because of the higher speed of the car, which leads to a more rapid decceleration, hence a larger impact force, during collision.

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