Question

15. An object of mass 1 kg travelling in a straight line with a velocity
of 10 m s' collides with, and sticks to, a stationary wooden
block of mass 5 kg. Then they both move off together in the
same straight line. Calculate the total momentum just before
the impact and just after the impact. Also, calculate the velocity
of the combined object.​

Answer 1

Given :

• Mass of object A = 1 kg
• Velocity of object A = 10 m/s
• Mass of object B = 5 kg
• Velocity of object B = 0 m/s (It is stationary)

To find :

• Total momentum before impact
• Total momentum after impact
• Velocity of combined object

According to the question,

➝ Momentum of object A = m × v

➝ Momentum of object A = 1 × 10

➝ Momentum of object A = 10 kg m/s

➝ Momentum of object B = m × v

➝ Momentum of object B = 5 × 0

➝ Momentum of object B = 0 kg m/s

.°. Total momentum before collision = 10 kg m/s + 0 kg m/s

➝ 10 kg m/s

Now,

➝ Total mass = 1 kg + 5 kg

➝ Total mass = 6 kg

➝ Momentum after collision = m × v

➝ Momentum after collision = 6 × v

➝ Momentum after collision = 6v

So,

➝ Momentum before collision = Momentum after collision

➝ 10 = 6 × v

➝ 10 ÷ 6 = v

➝ 1.67 = v

• So, the velocity of combined object is 1.67 m/s.

____________________

Answer 2

Given

An  object of mass 1 kg travelling in a straight line with a velocity

of 10 m s' collides with, and sticks to, a stationary wooden

block of mass 5 kg. Then they both move off together in the

same straight line

To Find

Total momentum before impact

Total momentum after impact

Velocity of combined object

Solution

Let the two object be object a and object b

$\implies$ Momentum (a) = m × v

$\implies$Momentum (a) = 1 × 10

$\implies$momentum (a) = 10 kgm/s

Now

Since velocity of object b is 0 So, The momentum will be 0

$\implies$Total Momentum = 10 kgm/s

Now

$\implies$Momentum after it collides = m × v

$\implies$Momentum after collides = 6 × v

$\implies$Momentum after collides = 6v

Now

Since mass remain same. So,

Momentum before collision = Momentum after collision

$\implies$10 = 6v

$\implies$10/6 = v

$\implies$1.66 = v