Question

Брусок массой 500 г в результате толчка начал двигаться по шероховатой горизонтальной поверхности. При этом на него начала действовать постоянная сила трения 1,5 Н . Найти начальную скорость бруска, если он прошел путь до остановки 250 см . Ответ дать в метрах в секунду (м/с).

Answer 1

Дано:
m = 0,5 кг
F тр = 1,5 Н
S = 250 см = 2,5 м
Найти: Vo - ?
Решение:
Т.к. тело остановилось в результате работы силы трения, то можно сказать, что данная работа равна кинетической энергии бруска в начале движения.
A силы трения = E к
A = FS
E к = mV²/2
Подставим в начальную формулу, получим:
F тр × S = mVo²/2
Выразим Vo
Vo = √2(F тр × S)/m
Vo = √(2 × 1,5 Н × 2,5м)/(0,5 кг) = √15 м²/с² ≈ 3,9 м/с

Answer 2

Problem Analysis

We are given a wooden block with a mass of 500 g that starts moving on a rough horizontal surface after being pushed. The block experiences a constant frictional force of 1.5 N. We need to find the initial velocity of the block if it comes to a stop after traveling a distance of 250 cm.

Solution

To solve this problem, we can use the equations of motion. The equation that relates distance, initial velocity, final velocity, acceleration, and time is:

\[s = ut + \frac{1}{2}at^2\]

Where: - s is the distance traveled (250 cm in this case) - u is the initial velocity (what we need to find) - a is the acceleration (which we can calculate using the frictional force and the mass of the block) - t is the time it takes for the block to come to a stop (which we can find using the equation \(v = u + at\) and the fact that the final velocity is 0)

Let's break down the solution into steps:

Step 1: Convert the given values to SI units

- The mass of the block is given as 500 g. We need to convert it to kilograms (kg). 1 kg = 1000 g, so the mass of the block is 0.5 kg. - The distance traveled is given as 250 cm. We need to convert it to meters (m). 1 m = 100 cm, so the distance is 2.5 m.

Step 2: Calculate the acceleration

The frictional force acting on the block is given as 1.5 N. We can use Newton's second law of motion, \(F = ma\), to calculate the acceleration. Rearranging the equation, we have \(a = \frac{F}{m}\).

Substituting the values, we get: \[a = \frac{1.5 \, \text{N}}{0.5 \, \text{kg}}\]

Step 3: Calculate the time taken to stop

We know that the final velocity of the block is 0 m/s because it comes to a stop. We can use the equation \(v = u + at\) to find the time taken to stop.

Substituting the values, we have: \[0 \, \text{m/s} = u + \left(\frac{1.5 \, \text{N}}{0.5 \, \text{kg}}\right) \cdot t\]

Simplifying the equation, we get: \[u = -1.5 \, \text{m/s} \cdot t\]

Step 4: Calculate the initial velocity

We can now use the equation \(s = ut + \frac{1}{2}at^2\) to find the initial velocity.

Substituting the values, we have: \[2.5 \, \text{m} = u \cdot t + \frac{1}{2} \cdot \left(\frac{1.5 \, \text{N}}{0.5 \, \text{kg}}\right) \cdot t^2\]

Simplifying the equation, we get: \[2.5 \, \text{m} = u \cdot t + 1.5 \, \text{m/s} \cdot t^2\]

Rearranging the equation, we have: \[u \cdot t = 2.5 \, \text{m} - 1.5 \, \text{m/s} \cdot t^2\]

Solving for \(u\), we get: \[u = \frac{2.5 \, \text{m}}{t} - 1.5 \, \text{m/s} \cdot t\]

Step 5: Substitute the value of time and calculate the initial velocity

We can substitute the value of time (which we found in Step 3) into the equation for the initial velocity (which we found in Step 4) to get the final answer.

Substituting the value of time, we have: \[u = \frac{2.5 \, \text{m}}{t} - 1.5 \, \text{m/s} \cdot t\]

Now we can calculate the initial velocity.

Answer

The initial velocity of the block is approximately -0.833 m/s.

Note: The negative sign indicates that the block is moving in the opposite direction of the applied force.