Question

С вершины наклонной плоскости высотой 5 м и углом наклона к горизонту 45o начинает соскальзывать тело. Определите скорость тела в конце спуска, если коэффициент трения тела о плоскость 0,19. Прошу Вас написать подробное решение.

Answer 1

Держите задачку по физике

Answer 2

Problem Analysis

We are given a inclined plane with a height of 5 m and an angle of inclination to the horizontal of 45 degrees. A body starts sliding down the plane, and we need to determine the velocity of the body at the end of the descent. The coefficient of friction between the body and the plane is 0.19.

Solution

To solve this problem, we can use the principles of Newtonian mechanics and the laws of motion. Let's break down the solution into steps:

Step 1: Determine the acceleration of the body The acceleration of the body can be calculated using the component of the gravitational force acting along the inclined plane. The formula for the acceleration is given by:

a = g * sin(θ)

where: - a is the acceleration - g is the acceleration due to gravity (approximately 9.8 m/s^2) - θ is the angle of inclination (45 degrees)

Using this formula, we can calculate the acceleration of the body.

Step 2: Calculate the frictional force The frictional force acting on the body can be calculated using the formula:

F_friction = μ * N

where: - F_friction is the frictional force - μ is the coefficient of friction (0.19) - N is the normal force

The normal force can be calculated using the formula:

N = m * g * cos(θ)

where: - m is the mass of the body - g is the acceleration due to gravity (approximately 9.8 m/s^2) - θ is the angle of inclination (45 degrees)

Using these formulas, we can calculate the frictional force acting on the body.

Step 3: Calculate the net force The net force acting on the body can be calculated by subtracting the frictional force from the component of the gravitational force along the inclined plane. The formula for the net force is:

F_net = m * a - F_friction

where: - F_net is the net force - m is the mass of the body - a is the acceleration of the body - F_friction is the frictional force

Using this formula, we can calculate the net force acting on the body.

Step 4: Calculate the velocity at the end of the descent The final velocity of the body can be calculated using the formula:

v^2 = u^2 + 2 * a * s

where: - v is the final velocity - u is the initial velocity (assumed to be 0 m/s) - a is the acceleration of the body - s is the distance traveled (equal to the height of the inclined plane, which is 5 m)

Using this formula, we can calculate the final velocity of the body.

Detailed Solution

Let's calculate the values step by step:

Step 1: Determine the acceleration of the body Using the formula a = g * sin(θ), where g is the acceleration due to gravity (approximately 9.8 m/s^2) and θ is the angle of inclination (45 degrees), we can calculate the acceleration:

a = 9.8 * sin(45) a ≈ 6.93 m/s^2 Step 2: Calculate the frictional force Using the formula F_friction = μ * N, where μ is the coefficient of friction (0.19) and N is the normal force, we can calculate the frictional force. The normal force can be calculated using the formula N = m * g * cos(θ), where m is the mass of the body, g is the acceleration due to gravity (approximately 9.8 m/s^2), and θ is the angle of inclination (45 degrees):

N = m * g * cos(45) N = m * 9.8 * cos(45) N ≈ 6.93 * m Substituting the value of N into the formula for frictional force:

F_friction = 0.19 * (6.93 * m) F_friction ≈ 1.32 * m Step 3: Calculate the net force Using the formula F_net = m * a - F_friction, where m is the mass of the body, a is the acceleration of the body, and F_friction is the frictional force, we can calculate the net force acting on the body:

F_net = m * 6.93 - 1.32 * m F_net = 5.61 * m Step 4: Calculate the velocity at the end of the descent Using the formula v^2 = u^2 + 2 * a * s, where v is the final velocity, u is the initial velocity (assumed to be 0 m/s), a is the acceleration of the body, and s is the distance traveled (equal to the height of the inclined plane, which is 5 m), we can calculate the final velocity of the body:

v^2 = 0^2 + 2 * 6.93 * 5 v^2 = 69.3 v ≈ 8.33 m/s Therefore, the velocity of the body at the end of the descent is approximately 8.33 m/s.

Please note that this solution assumes ideal conditions and neglects factors such as air resistance.