Question

1.Тележка массой m1= 20 кг движется прямолинейно по горизонтальному пути со скоростью v1= 2,8 м\с. В какой-то момент на нее вертикально падает мешок m2=30 кг. Чему равна скорость дальнейшего движения тележки с мешком на ней? 2.Ученик массой m1=50 кг бежит со скоростью v1=6 м\с, догнав тележку m2=30 кг,движущуюся со скоростью v2= 2 м\с,вскакивает а нее. Определите скорость тележки с учеником.

Answer 1

1)p1=p2
m1v1=(m1+m2) v2
v2=m1v1/m1+m2=20*2.8/50= 1,12м/с
2)v=m1v1+m2v2/m1+m2=360/80=4.5

Answer 2

Task 1: Тележка массой m1 = 20 кг движется прямолинейно по горизонтальному пути со скоростью v1 = 2,8 м/с. В какой-то момент на нее вертикально падает мешок m2 = 30 кг. Чему равна скорость дальнейшего движения тележки с мешком на ней?

To find the velocity of the cart with the bag on it, we can use the principle of conservation of momentum. The initial momentum of the cart before the bag falls on it is equal to the final momentum of the system (cart + bag) after the bag falls.

The initial momentum of the cart is given by the product of its mass (m1) and velocity (v1). The final momentum of the system is given by the product of the total mass (m1 + m2) and the final velocity (v).

According to the principle of conservation of momentum, the initial momentum is equal to the final momentum:

m1 * v1 = (m1 + m2) * v

Substituting the given values:

m1 = 20 kg v1 = 2.8 m/s m2 = 30 kg

We can calculate the final velocity (v) using the formula:

v = (m1 * v1) / (m1 + m2)

Plugging in the values:

v = (20 kg * 2.8 m/s) / (20 kg + 30 kg)

Calculating the result:

v = 56 kg·m/s / 50 kg

v ≈ 1.12 m/s.

Therefore, the velocity of the cart with the bag on it is approximately 1.12 m/s.

Task 2: Ученик массой m1 = 50 кг бежит со скоростью v1 = 6 м/с, догнав тележку m2 = 30 кг, движущуюся со скоростью v2 = 2 м/с, вскакивает на нее. Определите скорость тележки с учеником.

To determine the velocity of the cart with the student on it, we can again use the principle of conservation of momentum. The initial momentum of the student before jumping onto the cart is equal to the final momentum of the system (student + cart) after the student jumps.

The initial momentum of the student is given by the product of their mass (m1) and velocity (v1). The initial momentum of the cart is given by the product of its mass (m2) and velocity (v2). The final momentum of the system is given by the product of the total mass (m1 + m2) and the final velocity (v).

According to the principle of conservation of momentum, the initial momentum is equal to the final momentum:

(m1 * v1) + (m2 * v2) = (m1 + m2) * v

Substituting the given values:

m1 = 50 kg v1 = 6 m/s m2 = 30 kg v2 = 2 m/s

We can calculate the final velocity (v) using the formula:

v = ((m1 * v1) + (m2 * v2)) / (m1 + m2)

Plugging in the values:

v = ((50 kg * 6 m/s) + (30 kg * 2 m/s)) / (50 kg + 30 kg)

Calculating the result:

v = (300 kg·m/s + 60 kg·m/s) / 80 kg

v ≈ 4.5 m/s.

Therefore, the velocity of the cart with the student on it is approximately 4.5 m/s.