Question

Конькобежец массой 60 кг, стоя на коньках на льду, бросает вперёд в горизонтальном направлении предмет массой 1 кг и откатывается назад на 40 см. Коэффициент трения коньков о лёд - 0,02. Найдите скорость, с которой был брошен предмет.

Answer 1

m1 = 60кг

m2 = 1кг

S1 = 0.4м

f = 0.02

g = 9.8м/с²

v2 = ?

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На конькобежца действует только сила трения Fтр = -m1·gf в направлении, противоположном движению. поэтому по 2-му закону Ньютона

m1·a = -Fтр

или

m1·a = - m1·gf

ускорение: a = - gf

скорость v1(t) = v1₀ - gft

В конце пути конькобежец останавливается, поэтому v1(t)  = 0,

или v1₀ - gft = 0,

откуда t = v1₀/gf.

Длина отката S1(t) = v1₀·t - 0.5gft²

в момент остановки (при = t = v1₀/gf)

S1(t) = S1 = v1₀· (v1₀/gf) - 0.5gf·(v1₀/gf)² = 0.5·v1₀²/gf, откуда

v1₀ = √(2gf·S1) = √(2·9.8·0.02·0.4) = √0,1568 ≈ 0,396(м/с)

В начальный момент движения конькобежца его импульс равен импульсу брошенного предметаа. т.е.

m2·v2 = m1·v1₀, откуда

v2 = m1·v1₀/m2 = 60· 0,396/1 ≈ 23,76(м/с)

Answer 2

Calculating the Speed of the Thrown Object

To calculate the speed with which the object was thrown, we can use the principles of conservation of momentum and the work-energy principle.

Given: - Mass of the skater, m1 = 60 kg - Mass of the thrown object, m2 = 1 kg - Displacement of the skater, d = 40 cm = 0.4 m - Coefficient of friction between the skates and the ice, μ = 0.02

First, we can calculate the initial velocity of the skater after throwing the object using the conservation of momentum.

Conservation of Momentum: The initial momentum of the skater and the object is equal to the final momentum of the skater after throwing the object.

Let v1 be the initial velocity of the skater and v2 be the velocity of the thrown object.

The initial momentum = m1 * v1 The final momentum = (m1 + m2) * v2

Using conservation of momentum: m1 * v1 = (m1 + m2) * v2 v1 = ((m1 + m2) * v2) / m1

Next, we can calculate the work done by friction to find the initial velocity of the skater.

Work-Energy Principle: The work done by friction is equal to the change in kinetic energy of the skater.

The work done by friction = Force of friction * displacement The force of friction = coefficient of friction * normal force The normal force = m1 * g, where g is the acceleration due to gravity (approximately 9.81 m/s^2)

The work done by friction = μ * m1 * g * d

The change in kinetic energy = 0.5 * m1 * v1^2

Setting the work done by friction equal to the change in kinetic energy: μ * m1 * g * d = 0.5 * m1 * v1^2

Solving for v1, we can find the initial velocity of the skater.

Finally, we can calculate the speed with which the object was thrown using the initial velocity of the skater and the velocity of the thrown object.

Calculating the Speed of the Thrown Object: The speed with which the object was thrown, v2, is equal to the initial velocity of the skater, v1, minus the velocity of the skater after throwing the object.

Let's calculate the initial velocity of the skater and the speed with which the object was thrown.