A 21.0 kg body is moving in the direction of the positive x axis with a speed of

Question

A 21.0 kg body is moving in the direction of the positive x axis with a speed of 100.0 m/s when, owing to an internal explosion, it breaks into three parts. One part, whose mass is 7.00 kg, moves away from the point of explosion with a speed of 180 m/s in the direction of the positive y axis. A second fragment, with a mass of 4.00 kg, moves in the direction of the negative x axis with a speed of 250 m/s. What is the velocity of the third fragment? What are the magnitude and direction (in degrees) of this velocity? What is the change in mechanical energy from before to after the explosion? Ignore effects due to gravity.

Explanation / Answer

m = 21.0 kg
v = 100.0 i^ m/s

m1 = 7.0 kg
v1 = 180 j^ m/s

m2 = 4.0 kg
v2 = - 250.0 i^ m/s

m3 = 21.0 - 7.0 - 4.0 = 10.0 kg
v3 = ?

Using Momentum conservation,
In X axis,
21.0 * 100.0 = - 4.0 * 250 + 10.0 * v3
v3 =  310 i^ m/s

In Y axis,
0 = 7.0 * 180 + 10.0 * v3
v3 = - 126 j^ m/s

v3 =  310 i^ - 126 j^ m/s

|v3| = sqrt(310^2 + 126^2)
|v3| = 334.6 m/s

Direction = tan^-1(126/310)
Direction = 22.12o Clockwise from +ve x axis !!

Initial Mechanical Energy = 1/2*m*v^2
Ei = 1/2 * 21.0 * 100.0^2
Ei = 105000 J

Final Mechanical Energy = 1/2* (m1*v1^2 + m2*v2^2 + m3*v3^2)
Ef = 1/2 * (7.0 * 180.0^2 + 4.0*250.0^2 + 10*334.6^2)
Ef = 798185.8 J

Change in Mechanical Energy = 798185.8 - 105000 = 693185.8 J

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.