A 50-g bullet with a speed of 10 m/s hits into a sandbag hanging from the ceiling and embeds into it. The sandbag is at rest before the collision and gain a speed of 0.2 m/s afterwards. How much does the sandbag weigh?

momentum is conserved

initial momentum (bullet) , equals final momentum (bullet + sandbag)

50 g * 10 m/s = (S + 50 g) * 0.2 m/s

do you need to differentiate between mass and weight?

Given:

M1 = 0.05 kg, V1 = 10 m/s.
M2 = ?, V2 = 0.
V3 = Velocity of M1 after collision.
V4 = 0.2 m/s = velocity of M2 after collision.

Momentum before = Momentum after.
M1*V1 + M2*V2 = M1*V3 + M2*V4,
0.05*10 + M2*0 = 0.05*0 + M2*0.2,
0.5 = 0.2M2,
M2 = 2.5 kg. = Wt. of sandbag.

To find the weight of the sandbag, we need to make use of the principle of conservation of momentum.

The momentum before the collision is given by the product of the mass and velocity of the bullet:
Momentum_before = mass_bullet * velocity_bullet

The momentum after the collision is given by the product of the mass and velocity of the bullet-sandbag system:
Momentum_after = (mass_bullet + mass_sandbag) * velocity_after

According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore, we can equate the two equations:

mass_bullet * velocity_bullet = (mass_bullet + mass_sandbag) * velocity_after

Now let's substitute the given values:
mass_bullet = 50 g = 0.05 kg (converting grams to kilograms)
velocity_bullet = 10 m/s
velocity_after = 0.2 m/s

0.05 kg * 10 m/s = (0.05 kg + mass_sandbag) * 0.2 m/s

0.5 kg = (0.05 kg + mass_sandbag) * 0.2 m/s

0.5 kg = 0.01 kg + 0.2 * mass_sandbag

0.49 kg = 0.2 * mass_sandbag

Dividing both sides by 0.2:
mass_sandbag = 0.49 kg / 0.2 = 2.45 kg

Therefore, the sandbag weighs 2.45 kg.

To determine the weight of the sandbag, we can use the concept of conservation of momentum.

Momentum is a vector quantity that depends on an object's mass and velocity. In this scenario, we have a bullet with mass (m1) and initial velocity (v1), and a sandbag with an unknown mass (m2) and final velocity (v2).

First, we calculate the initial momentum (p1) of the bullet:
p1 = m1 * v1

Next, after the collision, the bullet is embedded in the sandbag, so their final velocity is the same (v2). The momentum of the sandbag with the bullet is given by:
p2 = (m1 + m2) * v2

According to the conservation of momentum principle, the total momentum before and after the collision should be the same. Therefore, we can equate the two momentum values:
p1 = p2
m1 * v1 = (m1 + m2) * v2

Now we can substitute the given values into the equation:
50 g = 0.05 kg (since 1 g = 0.001 kg)
v1 = 10 m/s
v2 = 0.2 m/s

Plugging in these values, we get:
0.05 kg * 10 m/s = (0.05 kg + m2) * 0.2 m/s

Simplifying the equation:
0.5 kg = 0.01 kg + 0.2 m2
0.49 kg = 0.2 m2

Finally, solving for m2 (mass of the sandbag):
m2 = 0.49 kg / 0.2 kg/m2
m2 = 2.45 kg

Therefore, the weight of the sandbag is 2.45 kg.