A 10.0-g marble slides to the left with a velocity of magnitude 0.450 m/s on the

Question

A 10.0-g marble slides to the left with a velocity of magnitude 0.450 m/s on the frictionless, horizontal surface of an icy, New York sidewalk and has a head-on, elastic collision with a larger 35.0-g marble sliding to the right with a velocity of magnitude 0.250 m/s.

(a) Find the velocity of each marble (magnitude and direction) after the collision. (Since the collision is head-on, all the motion is along a line. Take right as the positive x direction.)
  m/s (smaller marble)
m/s (larger marble)

(b) Calculate the change in momentum (that is, the momentum after the collision minus the momentum before the collision) for each marble.
kg·m/s (smaller marble)
kg·m/s (larger marble)

(c) Calculate the change in kinetic energy (that is, the kinetic energy after the collision minus the kinetic energy before the collision) for each marble.
J (smaller marble)
J (larger marble)

Explanation / Answer

here,

mass of smaller marble , m = 10 g

m = 0.01 g

mass of larger marble , M = 35 g

M = 0.035 Kg

speed of smaller and larger marbles , u1 = - 0.45 m/s and u2 = 0.25 m/s

let the speed of smaller and larger marbles after the collison be v1 and v2

using conservation of momentum ,

m * u1 + M * u2 = m * v1 + M * v2

- 0.01 * 0.45 + 0.035 * 0.25 = 0.01 * v1 + 0.035 * v2 ...(1)

using conservation of kinetic energy'

0.5 *m * u1^2 +0.5 * M * u2^2 = 0.5 * m * v1^2 + 0.5 * M * v2^2

0.01 * 0.45^2 + 0.035 * 0.25^2 = 0.01 * v1^2 + 0.035 * v2^2 ....(2)

from eqaution (1) and (2)

v1 = 0.64 m/s

v2 = - 0.06 m/s

(a)

the velocity of larger marble is - 0.06 m/s

the velocity of smaller marble is 0.64 m/s

(b)

change in momentum for smaller , Ps = m*(v1 - u1)

Ps = 0.01 * (0.64 + 0.45)

Ps = 0.011 kg .m/s

change in momentum for larger , Pl = M*(v2 - u2)

Pl = 0.035 * (- 0.06 - 0.25)

Pl = 0.01085 kg .m/s

(c)

change in kinetic energy for smaller , KEs = 0.5 * m*(v1^2 - u1^2)

KEs = 0.5* 0.01 * (0.64^2 - 0.45^2)

KEs = 1.04 * 10^-3 J

change in kinetic energy for larger , KEl = 0.5 * M*(v2^2 - u2^2)

KEl = 0.5* 0.035 * (0.06^2 - 0.25^2)

KEl = 1.03 * 10^-3 J

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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