The tank of a sprinkler weighing 4 tons contains water with a volume of 4 m3. What is the momentum

The tank of a sprinkler weighing 4 tons contains water with a volume of 4 m3. What is the momentum of the machine; a) when the machine moves to the irrigation site at a speed of 18 km / h; b) when the car is moving at a speed of 54 km / h, having used up all the water?

mm = 4 t = 4000 kg.

Vw = 4 m3.

ρ = 1000 kg / m3.

v1 = 18 km / h = 5 m / s.

v2 = 54 km / h = 15 m / s.

p1 -?

p2 -?

The momentum of a body p is a vector physical quantity equal to the product of the mass m of the body by the speed of its movement v: p = m * v. The momentum of the body p is directed in the same way as the speed of movement v of the body.

The momentum of the machine without water p2 is expressed by the formula: p2 = mm * v2.

p2 = 4000 kg * 15 m / s = 60,000 kg * m / s.

The impulse of the machine with water p1 is expressed by the formula: p1 = (mm + mv) * v1.

We find the mass of water mw by the formula: mw = Vw * ρ.

р1 = (mm + Vw * ρ) * v1.

p1 = (4000 kg + 4 m3 * 1000 kg / m3) * 5 m / s = 40,000 kg * m / s.

Answer: p1 = 40,000 kg * m / s, p2 = 60,000 kg * m / s.