Sppose a 1.0-kg cart with low-friction wheels is traveling at 1.0 m/s rightward just before it collides with a similar 2.0-kg cart at rest. Just after the collision, the more massive cart is observed to be moving rightward with a speed of 2/3 m/s.

a. What impulse was delivered to the massive cart?
b. What impulse was delivered to the light cart?
c. What is the light cart's final momentum?
d. What is that cart's final velocity after the collision? Answer

a) 1.33kgm/s, b) - 0.67kg/m, c) 0.33 kgm/s, d) 0.33 m/s

Explanation:

mass of first cart = 1kg, mass of second cart = 2kg, initial velocity of first cart before collision= 1m/s,

initial velocity of second cart before collision = 0m/s ( since the object is that rest).

Final velocity of the first cart after collision =?

Final velocity of the second cart after collision = 2/3 m/s.

Question d)

Note, momentum = mass × velocity,

impulse = change in momentum = final momentum - initial momentum

For an isolated system, the vector sum of momentum before collision equals the vector sum of momentum after collision.

Before collision

Momentum of the first cart = 1×1 = 1kgm/s

Momentum of the second cart = 2×0= 0

Sum of momentum before collision =2kgm/s.

Please note that after collision, the first cart will love in the opposite direction of it initial motion thus making it have a negative value of momentum.

After collision

Momentum of first object =1×-v = - v

Momentum of the second object = 2×2/3 = 4/3

Hence we have That

1 + 0 = - v + 4/3

By collecting like terms, we have that

1 = - v + 4/3

v = 4/3 - 1

v = 1/3 m/s = 0.33m/s

Question a)

Impulse delivered to the larger cart = equals change in momentum on the larger cart.

Mass = 2kg, initial velocity = 0, final velocity = 2/3 m/s

Change in momentum = mass (final velocity - initial velocity)

Change in momentum = 2 ( 2/3 - 0)

Change in momentum = 4/3 kgm/s = 1.33kgm/s.

Question b)

Mass of light cart = 1kg, initial velocity =1 m/s, final velocity = 1/3

Change in momentum = 1 ( 1/3 - 1)

Change in momentum = 1(-2/3) = - 0.67 kgm/s

Question c)

Final momentum of light cart = mass * final velocity

Final momentum of light cart = 1 * 1/3 = 1/3 = 0.33 kgm/s.

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