Question

Тело свободно падает без начальной скорости. Изменение модуля импульса этого тела за промежуток времени 2 с равно 10 кг м/с. Чему равна масса тела? Сопротивлением воздуха можно пренебречь.

Answer 1

Ответы с решением в приложенном файле:

Answer 2

Calculation of the Mass of the Falling Object

To determine the mass of the falling object, we can use the concept of impulse. Impulse is defined as the change in momentum of an object and is equal to the product of the force applied to the object and the time interval over which the force is applied.

In this case, the falling object is initially at rest, so its initial momentum is zero. The change in momentum of the object over a time interval of 2 seconds is given as 10 kg·m/s.

Using the equation for impulse, we can write:

Impulse = Change in momentum = Force × Time

Since the force acting on the object is due to gravity, we can substitute the formula for momentum (mass × velocity) into the equation:

Force × Time = Mass × Change in velocity

Since the object is falling freely without any initial velocity, the change in velocity is equal to the final velocity. Therefore, we can rewrite the equation as:

Force × Time = Mass × Final velocity

Since the force acting on the object is the gravitational force, we can substitute the formula for force (mass × acceleration due to gravity) into the equation:

(Mass × Acceleration due to gravity) × Time = Mass × Final velocity

The mass of the object cancels out, and we are left with:

Acceleration due to gravity × Time = Final velocity

Now, we can solve for the final velocity using the equation of motion for free fall:

Final velocity = Initial velocity + (Acceleration due to gravity × Time)

Since the object is initially at rest, the initial velocity is zero. Therefore, the equation simplifies to:

Final velocity = Acceleration due to gravity × Time

Substituting the given values, we have:

Final velocity = 9.8 m/s² × 2 s = 19.6 m/s

Now, we can substitute the final velocity back into the equation to find the mass of the object:

(Mass × Acceleration due to gravity) × Time = Mass × 19.6 m/s

Simplifying the equation, we have:

Mass × 9.8 m/s² × 2 s = Mass × 19.6 m/s

The time cancels out, and we are left with:

Mass × 9.8 m/s² = Mass × 19.6 m/s

Dividing both sides of the equation by 9.8 m/s², we get:

Mass = 19.6 m/s / 9.8 m/s² = 2 kg

Therefore, the mass of the falling object is 2 kg.