An m = 6.70-kg clay ball is thrown directly against a perpendicular brick wall a

Question

An m = 6.70-kg clay ball is thrown directly against a perpendicular brick wall at a velocity of 22.0 m/s and shatters into three pieces, which all fly backward, as shown in the figure. The wall exerts a force on the ball of 2630 N for 0.110 s. One piece of mass m1 = 2.70 kg travels backward at a velocity of 10.4 m/s and an angle of = 32.0 above the horizontal. A second piece of mass m2 = 1.70 kg travels at a velocity of 8.10 m/s and an angle of 28.0 below the horizontal.
a) What is the velocity of the third piece?

b) What is the direction of the third piece?

An m = 6.70-kg clay ball is thrown directly against a perpendicular brick wall at a velocity of 22.0 m/s and shatters into three pieces, which all fly backward, as shown in the figure. The wall exerts a force on the ball of 2630 N for 0.110 s. One piece of mass m1 = 2.70 kg travels backward at a velocity of 10.4 m/s and an angle of = 32.0½ above the horizontal. A second piece of mass m2 = 1.70 kg travels at a velocity of 8.10 m/s and an angle of 28.0½ below the horizontal. a) What is the velocity of the third piece? b) What is the direction of the third piece?

Explanation / Answer

Initial momentum must be equal to terminal momentum at both x and y directions.
Pxi = Pxt and Pyi = Pyt


Pxi = m*Vi = 6.9*22=(+)151.8 kg*m/s
The impact of the wall = F*dt=2640*0.110=(-)290.4 kg*m/s

Pxt=-290.4+151.8=(-)138.6 (It means -x direction)

At this point,the ball shatters in three peces.

m1= 2.9 kg , m2=1.9 kg , m3=3.1 kg

Total Px must be equal to Pxt and total Py must be equal to zero(Because there was no component of momentum vector in the first place)

Px1=m1*V1*cos32=(-)26.56 kg*m/s
Px2=m2*V2*cos28=(-)13.59 kg*m/s

Px3=Pxt - (Px1 + Px2) =(-)98.45 kg*m/s


Py1=m1*V1*sin32=(+)16.597 kg*m/s
Py2=m2*V2*sin28=(-)7.225 kg*m/s

Py3=Pyt - (Py1 + Py2)=(-)9.372 kg*m/s


P3=((Px3)^2 + (Py3)^2)^1/2 = 98.895 kg*m/s

a) P3=m3*V3 ====> V3=31.902 m/s

b) Py3/Px3 = tanx =====> x= (-)5.4379 dergrees below from the horizontal.. (Don't forget the minus sign! )

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