Final answer:
The accelerated motion of a box sliding on a rough surface is determined by the net force acting on it, which is the difference between the force of gravity and the force of friction.
Step-by-step explanation:
In this question, we have a 2.0kg box that is released from rest at a height of 0.25m on a frictionless ramp. The box then slides from the ramp onto a rough horizontal surface with a friction coefficient of 0.50.
To find the acceleration of the box on the rough surface, we need to calculate the net force acting on the box. The net force is equal to the force of gravity pulling the box down the ramp minus the force of friction opposing its motion.
The force of gravity can be calculated using the formula F = m * g, where m is the mass of the box (2.0kg) and g is the acceleration due to gravity (10 m/s²). Plugging in the values, we get F = 2.0kg * 10 m/s² = 20 N.
The force of friction can be calculated using the formula F = μ * N, where μ is the coefficient of friction (0.50) and N is the normal force.
The normal force is equal to the force of gravity acting perpendicular to the surface, which is the same as the weight of the box. So the normal force is 20 N. Plugging in the values, we get F = 0.50 * 20 N = 10 N.
The net force is therefore equal to the force of gravity minus the force of friction: Net force = 20 N - 10 N = 10 N.
Finally, using Newton's second law of motion (F = m * a), we can calculate the acceleration of the box. Plugging in the values, we get 10 N = 2.0kg * a. Solving for a, a = 10 N / 2.0kg = 5 m/s².