Question

На силы массой 40 кг действуют силы F 1 = 250 N и F₂ = 50 N, и противоположно направленная сила трения F = 100 N, которая тормозит тело. Определить ускорение тела. Какой скорости достигает тележка за 5 секунд

Answer 1

Ответ:

$a=5\frac{m}{s^2} \\V_{t=5}=25\frac{m}{s}$

Объяснение:

Распишем проекцию на ось Ox:
$Ox:F_1+F_2-F_T=ma_x$

Тележка ускоряется только по оси Ox, так что $a_x=a$, выразим:
$\left \{ {{F_1+F_2-F_T=ma_x} \atop {a_x=a}} \right. \\a=\frac{F_1+F_2-F_T}{m} \\a=\frac{250N+50N-100N}{40kg} \\a=5\frac{m}{s^2}$

Найдем скорость тела через 5 секунд после начала движения, если V₀ = 0:
$V_t=V_0+at\\V_t=V_0+\frac{F_1+F_2-F_T}{m} t\\V_{t=5}=0+\frac{250N+50N-100N}{40kg} *5s\\V_{t=5}=25\frac{m}{s}$

Answer 2

Given Information:

- Mass of the object (m) = 40 kg - Force 1 (F1) = 250 N - Force 2 (F2) = 50 N - Frictional force (F) = 100 N

Calculating Acceleration:

To determine the acceleration of the object, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it can be expressed as:

F_net = ma

Where: - F_net is the net force acting on the object - m is the mass of the object - a is the acceleration of the object

In this case, the net force acting on the object is the sum of the applied forces (F1 and F2) minus the frictional force (F):

F_net = F1 + F2 - F

Substituting the given values:

F_net = 250 N + 50 N - 100 N

Now, we can calculate the net force:

F_net = 200 N

Next, we can rearrange the equation to solve for acceleration:

a = F_net / m

Substituting the values:

a = 200 N / 40 kg

Calculating the acceleration:

a = 5 m/s^2

Therefore, the acceleration of the object is 5 m/s^2.

Calculating the Final Velocity:

To determine the final velocity of the object after 5 seconds, we can use the equation of motion:

v = u + at

Where: - v is the final velocity - u is the initial velocity (assumed to be 0 m/s) - a is the acceleration - t is the time

Substituting the given values:

v = 0 + (5 m/s^2) * 5 s

Calculating the final velocity:

v = 25 m/s

Therefore, the object reaches a velocity of 25 m/s after 5 seconds.

Note: The above calculations assume that the forces are constant and there are no other external factors affecting the motion of the object.