Question

Тело массой 5 кг под действием силы 10 н движется с ускорением вниз по наклонной плоскости с углом наклона 60° коэффициент трения 0,8 Найти ускоренное тела его скорость через 2 с после начала движения

Answer 1

Спасибо за интересную задачку.

Answer 2

Problem Analysis

We are given the following information: - Mass of the body, m = 5 kg - Force acting on the body, F = 10 N - Angle of inclination of the inclined plane, θ = 60° - Coefficient of friction, μ = 0.8 - Time, t = 2 s

We need to find: - Acceleration of the body, a - Velocity of the body after 2 seconds, v

To solve this problem, we can use Newton's second law of motion and the equations of motion.

Solution

# Step 1: Resolving forces

The force acting on the body can be resolved into two components: - The component parallel to the inclined plane, F_parallel = F * sin(θ) - The component perpendicular to the inclined plane, F_perpendicular = F * cos(θ)

# Step 2: Finding the normal force

The normal force, N, is the force exerted by the inclined plane perpendicular to the surface of contact. It is equal in magnitude and opposite in direction to the component of the weight of the body perpendicular to the inclined plane.

The weight of the body, W = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).

The component of the weight perpendicular to the inclined plane, W_perpendicular = m * g * cos(θ)

Therefore, the normal force, N = W_perpendicular = m * g * cos(θ)

# Step 3: Finding the frictional force

The frictional force, f, opposes the motion of the body and is given by the equation f = μ * N, where μ is the coefficient of friction.

Therefore, the frictional force, f = μ * N = μ * m * g * cos(θ)

# Step 4: Finding the net force

The net force acting on the body, F_net, is the vector sum of the parallel component of the force and the frictional force.

F_net = F_parallel - f

# Step 5: Finding the acceleration

Using Newton's second law of motion, F_net = m * a, we can solve for the acceleration, a.

a = F_net / m

# Step 6: Finding the velocity after 2 seconds

Using the equation of motion, v = u + a * t, where u is the initial velocity (which is 0 in this case), we can find the velocity of the body after 2 seconds.

v = a * t

Now, let's calculate the values.

Calculation

Given: - Mass of the body, m = 5 kg - Force acting on the body, F = 10 N - Angle of inclination of the inclined plane, θ = 60° - Coefficient of friction, μ = 0.8 - Time, t = 2 s

Using the equations mentioned above, we can calculate the values.

Step 1: Resolving forces F_parallel = F * sin(θ) = 10 * sin(60°) = 10 * 0.866 = 8.66 N F_perpendicular = F * cos(θ) = 10 * cos(60°) = 10 * 0.5 = 5 N

Step 2: Finding the normal force N = m * g * cos(θ) = 5 * 9.8 * cos(60°) = 5 * 9.8 * 0.5 = 24.5 N

Step 3: Finding the frictional force f = μ * N = 0.8 * 24.5 = 19.6 N

Step 4: Finding the net force F_net = F_parallel - f = 8.66 - 19.6 = -10.94 N (opposite direction of motion)

Step 5: Finding the acceleration a = F_net / m = -10.94 / 5 = -2.188 m/s^2 (negative sign indicates acceleration in the opposite direction of motion)

Step 6: Finding the velocity after 2 seconds v = a * t = -2.188 * 2 = -4.376 m/s

Answer

The acceleration of the body is -2.188 m/s^2 (opposite direction of motion) and the velocity of the body after 2 seconds is -4.376 m/s (opposite direction of motion).

Please note that the negative sign indicates the direction of motion, which is opposite to the direction of the force applied.