An object with a mass of 8.00 g is moving to the right at 14.0 cm/s when it is o

Question

An object with a mass of 8.00 g is moving to the right at 14.0 cm/s when it is overtaken by an object with a mass of 27.0 g moving in the same direction with a speed of 23.0 cm/s. If the collision is elastic, determine the speed of each object after the collision. 27.0-g object Incorrect: Your answer is incorrect. After establishing that energy and momentum are conserved, see if you can write a statement of conservation of momentum and a statement of conservation of energy. Each of these two statements will contain the two desired unknowns (final speed of the two masses) and may be solved simultaneously to obtain expressions which will allow us to determine the final speed of the two masses. cm/s 8.00-g object Incorrect: Your answer is incorrect. After establishing that energy and momentum are conserved, see if you can write a statement of conservation of momentum and a statement of conservation of energy. Each of these two statements will contain the two desired unknowns (final speed of the two masses) and may be solved simultaneously to obtain expressions which will allow us to determine the final speed of the two masses. cm/s

Explanation / Answer

Suppose after collision, speed of 8g mass is v1 and speed of 27g object is v2.

then for elastic collision,

speed of approch = speed of separation

23- 14 = v1 - v2

v1 = 9 + v2

now Applying momentum conservation for collision,

8 x 14 + 27 x 23 = 8v1 + 27v2

733 = 8(9 + v2) + 27v2

v2 = 18.9 cm/s ..........Speed of 27g object.

v1 = 18.9 + 9 = 27.9 cm/s .....Speed of 8g object/

-------------

KE of mass = m v^2 /2

Initial energy= (0.008 x 0.14^2 / 2) + (0.027 x 0.23^2 /2 )

= 7.93 x 10^-4 J

after collision,

KEf = (0.008 x 0.279^2 /2 ) + (0.027 x 0.189^2 / 2 ) = 7.93 x 10^-4 J

hence energy of system is conserved in the collision.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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