Question

Тело массой 0,2кг падает с высоты 1м с ускорением 8м/с2. Найти изменение импульса тела за время полета.

Answer 1

Импульс тела равен массе, умноженной на скорость: p=mv;
Уравнение движения падающего тела следующее: x=-1+0.5at^2; где a- ускорение тела.
x=-1+4t^2;
В момент падения x=0 значит получаем уравнение: -1+4t^2=0;
4t^2=1;
t^2=0.25;
t=SQRT(0.25);
t=0.5 c. (тело упадёт за полсекунды)
Уравнение для скорости тела: v(t)=x'(t)=8t;
Получаем изменение импульса тела за время полёта:
dp=p(0.5)-p(0);
dp=m(v(0.5)-v(0));
dp=0.2*(8*0.5-8*0);
dp=0.2*4;
dp=0.8 кгм/с

Answer 2

Calculation of Change in Momentum

To find the change in momentum of an object, we can use the formula:

Change in momentum = mass × change in velocity

In this case, the mass of the object is 0.2 kg and the acceleration due to gravity is 8 m/s². The object falls from a height of 1 m, so we need to find the final velocity of the object when it hits the ground.

To find the final velocity, we can use the equation of motion:

v² = u² + 2as

where: - v is the final velocity - u is the initial velocity (which is 0 m/s since the object is dropped) - a is the acceleration due to gravity (which is 9.8 m/s²) - s is the distance traveled (which is 1 m)

Plugging in the values, we can solve for v:

v² = 0² + 2 × 9.8 × 1 v² = 19.6 v ≈ 4.43 m/s

Now that we have the final velocity, we can calculate the change in velocity:

Change in velocity = final velocity - initial velocity Change in velocity = 4.43 - 0 Change in velocity = 4.43 m/s

Finally, we can calculate the change in momentum:

Change in momentum = mass × change in velocity Change in momentum = 0.2 kg × 4.43 m/s Change in momentum ≈ 0.886 kg·m/s

Therefore, the change in momentum of the object during its flight is approximately 0.886 kg·m/s.