Exercise 2. The barrier (8 points) A manufacturer of barriers for racing circuit

Question

Exercise 2. The barrier (8 points) A manufacturer of barriers for racing circuits is testing the impact absorption capabilities of its new product. A 1000 kg (nib) barrier of the new material is installed in a test room and the friction coefficient of the barrier with the floor is Mub = 0.8. A 100 kg (ms) steel block (considered infinitely rigid in comparison with the barrier) is accelerated by a hydraulic system which applies a constant force Fh = 1 kN for a time t1 of 3 seconds before releasing the block. The steel block slides on the floor with a friction coefficient of Mu = 0.1. After a rectilinear motion for a distance delta x2 = 2 m (still on the same floor) the steel block hits the barrier. At the end of the test the engineers find that the barrier has moved by delta xb = 10 cm. C. How much energy has been lost during the impact? D. Is there any problem with the barrier?

Explanation / Answer

a)force imparted on the steel block= 1000 N

acceleration=force/mass=10 m/s^2

as it is acted for 3 seconds, initial velocity achieved=acceleration*time=30 m/s

now as it slides on a floor with friction coefficient 0.1,

friction force on the block=0.1*normal force

=0.1*100*9.8=98 N

so deceleration=98/100=0.98 m/s^2

so as it travels 2 m, the velocity is reduced to v m/s(let)

then v^2-30^2=-2*0.98*2

v=29.935 m/s

now it is mentioned that the barrier has moved by 10 cm

then friction force on the barrier=0.8*1000*9.8

deceleration due to this friction force=0.8*9.8=7.84

so if initial speed of the barrier is v1,

then v1^2=2*7.84*0.1

v1=1.2522 m/s

then if after impact speed of the block is v2,

then conserving momentum,

100*29.935=100*v2+1000*1.2522

v2=17.413 m/s

so energy lost=initial energy of the block before impact-final energy of the block and barrier after impact

=0.5*100*29.935^2-0.5*1000*1.2522^2-0.5*100*17.413^2=2.886*10^4 J

b)there is exactl nothing defined as what can be a problem for the barrier

for example, if some specification is mentioned that the barrier should withstand this much pressure, then we can infer something from the information provided.

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