A 1.0kg box on a horizontal frictionless surface is accelerated by attaching and hanging a 1.5 kg
mass over a pulley. What is the acceleration of the box? (Remember both boxes are accelerated).
To find the acceleration of the box, we need to apply Newton's second law of motion.
First, let's denote the acceleration of the system as "a". We know that the 1.5 kg mass is pulling the 1.0 kg box, so the force acting on the box is equal to the force exerted by the 1.5 kg mass.
Let's analyze the forces on the two masses separately. For the 1.5 kg mass, the force pulling it downwards is equal to its weight, given by mass times gravity. Since the mass is 1.5 kg and the acceleration due to gravity is approximately 9.8 m/s²:
Force on 1.5 kg mass = (1.5 kg) × (9.8 m/s²) = 14.7 N
The force on the 1.0 kg box is equal to the tension in the rope. These two forces are connected by Newton's third law, which states that the force exerted by one object on another is equal in magnitude and opposite in direction to the force exerted by the second object on the first.
So the force on the 1.0 kg box is also 14.7 N, but in the opposite direction.
Using Newton's second law, we can express the equation as:
Force = mass × acceleration
For the 1.5 kg mass: 14.7 N = (1.5 kg) × a
For the 1.0 kg box: 14.7 N = (1.0 kg) × (-a) (opposite direction)
Simplifying these equations gives us:
1.5a = 14.7 (equation 1)
1.0a = 14.7 (equation 2)
Rearranging equation 1, we find:
a = 14.7 / 1.5 = 9.8 m/s²
Therefore, the acceleration of the box is 9.8 m/s².
Keep in mind that in problems like this, we assume there is no friction and that the pulley mass is negligible.