A block of mass 5 kg is placed on a rough inclined plane with an angle of 30 degrees. The coefficient of kinetic friction between the block and the plane is 0.2. Calculate the acceleration of the block as it slides down the plane.
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To calculate the acceleration of the block as it slides down the inclined plane, we need to consider the forces acting on the block.
1. Component of gravity parallel to the plane: The force of gravity acting on the block can be broken down into two components: one parallel to the inclined plane and one perpendicular to it. The component parallel to the plane is given by: F_parallel = m * g * sin(theta), where m is the mass (5 kg), g is the acceleration due to gravity (9.8 m/s^2), and theta is the angle of the inclined plane (30 degrees). Substituting these values into the equation, we get: F_parallel = 5 * 9.8 * sin(30) = 24.5 N.
2. Force of kinetic friction: The force of kinetic friction acting on the block is given by: F_friction = u * F_normal, where u is the coefficient of kinetic friction (0.2) and F_normal is the normal force acting on the block. Since the block is on an inclined plane, the normal force is given by: F_normal = m * g * cos(theta), where m is the mass (5 kg), g is the acceleration due to gravity (9.8 m/s^2), and theta is the angle of the inclined plane (30 degrees). Substituting these values into the equation, we get: F_normal = 5 * 9.8 * cos(30) = 42.62 N. Substituting the value of F_normal into the equation for F_friction, we get: F_friction = 0.2 * 42.62 = 8.52 N.
3. Net force: The net force acting on the block is given by: F_net = F_parallel - F_friction = 24.5 - 8.52 = 15.98 N.
4. Acceleration: The acceleration of the block can be calculated using Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration: F_net = m * a, where a is the acceleration. Substituting the values of F_net and m into the equation, we get: 15.98 = 5 * a. Solving for a, we find that the acceleration of the block is: a = 15.98 / 5 = 3.196 m/s^2.
Therefore, the acceleration of the block as it slides down the inclined plane is 3.196 m/s^2.
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