Question

Свинцовый шар массы m = 500 г, движущийся со скоростью υ = 10 м/с, соударяется с неподвижным шаром из воска, имеющим массу М = 200 г, после чего оба шара движутся вместе. Найти кинетическую энергию шаров после соударения.

Answer 1

Т.к. удар абсолютно неупругий: шары движутся вместе => часть кинетической энергии при ударе переходит в тепловую. А вот закон сохранения импульса действует, т.е. m*U=(m+M)*V  откуда  V=m*U/(m+M)=0.5*10/(0.5+0.2)=7.14[м/с]
Ек1=mV^2/2=0.5*7.14^2/2=12.74 [Дж]
Ek2=M*V^2/2=0.2*7.14*7.14/2=5.1[Дж]
Ek=Ek1+Ek2=17,84 [Дж]

Answer 2

Calculating Kinetic Energy After Collision

To calculate the kinetic energy of the two spheres after the collision, we can use the formula for kinetic energy:

Kinetic Energy (KE) = 0.5 * mass * velocity^2

First, let's calculate the initial kinetic energy of the lead sphere before the collision using the given mass and velocity: - Mass of lead sphere, m = 500 g = 0.5 kg - Velocity of lead sphere, υ = 10 m/s

Using the formula, the initial kinetic energy of the lead sphere is: KE_lead = 0.5 * 0.5 kg * (10 m/s)^2

Now, let's calculate the initial kinetic energy of the wax sphere, which is at rest: - Mass of wax sphere, M = 200 g = 0.2 kg - Since the wax sphere is at rest, its initial kinetic energy is 0.

After the collision, the two spheres move together with a common velocity. To find this common velocity, we can use the principle of conservation of momentum, which states that the total momentum of an isolated system remains constant if no external forces act on it.

The total momentum before the collision is the sum of the individual momenta of the lead and wax spheres: Initial momentum = m * υ_lead + M * υ_wax = 0.5 kg * 10 m/s + 0 * υ_wax

The total momentum after the collision is the sum of the individual momenta of the lead and wax spheres moving together at a common velocity, say V: Final momentum = (m + M) * V

By the principle of conservation of momentum, the initial and final momenta are equal: m * υ_lead + M * υ_wax = (m + M) * V

Solving for V, we can find the common velocity of the two spheres after the collision.

Finally, we can calculate the kinetic energy of the two spheres after the collision using the total mass (m + M) and the common velocity V.

Let's calculate the common velocity V and the kinetic energy of the two spheres after the collision.