A manufacturer of barriers for racing circuits is testing the impact absorption

Question

A manufacturer of barriers for racing circuits is testing the impact absorption capabilities of its new product. A 1000 kg (mb) barrier of the new material is installed in a test room and the friction coefficient of the barrier with the floor is mu b = 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 s =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. Which is the maximum speed reached by the steel block? How much energy is lost in friction before the impact? How much energy has been lost during the impact? 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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