Question

Координата движущего тела изменяется по закону х=4+3t-0.5t в квадрате,а проекция импульса по закону р=10-5t.найдите массу тела и действующую на него силу

Answer 1

Так как импульс изменяется по следующему закону:
$p=mv_o-vt$
А координата точки:
$x=x_o+v_ot+\cfrac{at^2}{2}$
Получаем, что $v_o=3$ тогда масса будет равна: $m=\cfrac{10}{3}$
Ускорение равно единице, значит сила действующая на тело равна:
$F=ma=\cfrac{10}{3}$
Ответ: 
$m\approx 3,3$ кг
$F\approx 3,3 H$

Answer 2

Given Information

We are given the following information: - The coordinate of the moving body changes according to the law: x = 4 + 3t - 0.5t^2. - The projection of the impulse follows the law: p = 10 - 5t.

Finding the Mass of the Body

To find the mass of the body, we need to use the equation relating impulse and momentum. The equation is given by:

p = m * v

Where: - p is the impulse - m is the mass of the body - v is the velocity of the body

In this case, we are given the equation for the projection of the impulse, p = 10 - 5t. To find the mass, we need to find the velocity first.

Finding the Velocity of the Body

To find the velocity of the body, we can differentiate the equation for the coordinate with respect to time (t). The derivative of x with respect to t gives us the velocity (v).

Differentiating the equation x = 4 + 3t - 0.5t^2 with respect to t, we get:

v = dx/dt = d/dt(4 + 3t - 0.5t^2)

Differentiating each term separately, we get:

v = 3 - t

Now that we have the velocity, we can substitute it into the equation for impulse to find the mass.

Finding the Mass

Substituting the velocity (v = 3 - t) into the equation for impulse (p = 10 - 5t), we get:

10 - 5t = m * (3 - t)

Expanding the equation, we get:

10 - 5t = 3m - mt

Rearranging the equation, we get:

5t - mt = 3m - 10

Factoring out the common terms, we get:

t(5 - m) = 3m - 10

Dividing both sides by (5 - m), we get:

t = (3m - 10) / (5 - m)

Now, we can solve this equation to find the value of m.

Finding the Force Acting on the Body

To find the force acting on the body, we can use Newton's second law of motion, which states that the force (F) acting on an object is equal to the rate of change of momentum (dp/dt).

In this case, the momentum (p) is given by p = 10 - 5t. To find the force, we need to differentiate the momentum with respect to time (t).

Differentiating the equation p = 10 - 5t with respect to t, we get:

dp/dt = d/dt(10 - 5t)

Differentiating each term separately, we get:

dp/dt = 0 - 5

Therefore, the force acting on the body is -5 N.

Summary

- The mass of the body can be found by solving the equation: t = (3m - 10) / (5 - m). - The force acting on the body is -5 N.

Please note that the given information and calculations are based on the provided equation and the laws of physics.