Question

Брусок массой 2 кг соскальзывает без начальной скорости с вершины гладкой наклонной плоскости.За время движения бруска равнодействующая всех сил,приложенных к нему,совершила работу 80 Дж. Пренебрегая сопротивлением воздуха и трением,определить высоту наклонной плоскости.

Answer 1

В этом случае работу А совершала только сила тяжести.А=mgh. Нам нужно найти высоту h. h=А /mg, то h=80/2*10 = 4 метра.

Answer 2

Problem Analysis

We are given a block with a mass of 2 kg that slides down a smooth inclined plane without any initial velocity. The resultant force acting on the block does work equal to 80 J during its motion. We need to determine the height of the inclined plane.

Solution

To solve this problem, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy. In this case, since the block starts from rest, the initial kinetic energy is zero. Therefore, the work done on the block is equal to its final kinetic energy.

The work done on the block is given as 80 J. We can calculate the final kinetic energy of the block using the formula:

Work done = Final kinetic energy

The kinetic energy of an object is given by the formula:

Kinetic energy = (1/2) * mass * velocity^2

Since the block starts from rest, its final velocity is also zero. Therefore, the final kinetic energy is zero. Hence, the work done on the block is also zero.

Now, let's consider the forces acting on the block as it slides down the inclined plane. The only force acting on the block is its weight, which can be decomposed into two components: one parallel to the inclined plane and one perpendicular to it.

The force parallel to the inclined plane is responsible for the acceleration of the block down the plane. The force perpendicular to the inclined plane does not contribute to the work done on the block since it is perpendicular to the displacement.

Since the block starts from rest, the initial velocity is zero, and the work done by the force parallel to the inclined plane is also zero. Therefore, the work done on the block is solely due to the force perpendicular to the inclined plane.

Let's denote the height of the inclined plane as 'h'. The work done by the force perpendicular to the inclined plane is equal to the product of the perpendicular force and the displacement, which is equal to the height of the inclined plane.

Work done = Force perpendicular * displacement

Since the work done is 80 J and the displacement is equal to the height of the inclined plane 'h', we have:

80 J = Force perpendicular * h

Now, let's calculate the force perpendicular to the inclined plane. The force perpendicular to the inclined plane is equal to the weight of the block, which is given by:

Force perpendicular = mass * acceleration due to gravity

Substituting the mass of the block (2 kg) and the acceleration due to gravity (9.8 m/s^2), we have:

Force perpendicular = 2 kg * 9.8 m/s^2

Now, we can substitute the value of the force perpendicular into the equation for the work done:

80 J = (2 kg * 9.8 m/s^2) * h

Simplifying the equation, we can solve for the height 'h':

h = 80 J / (2 kg * 9.8 m/s^2)

Calculation

Let's calculate the value of 'h':

h = 80 J / (2 kg * 9.8 m/s^2)

h = 4.08 meters

Answer

The height of the inclined plane is approximately 4.08 meters.