Final answer:
The acceleration of the cart in Box 1 can be found by using Newton's second law of motion. The weight of the falling block is equal to the force acting on the cart, and the acceleration can be calculated using the force-mass relationship. In this case, the acceleration is 19.6 m/s².
Step-by-step explanation:
The acceleration of the cart in Box 1 can be determined using Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the force acting on the cart is the weight of the falling block.
First, we need to calculate the weight of the block. Weight is given by the equation weight = mass * acceleration due to gravity.
Assuming the acceleration due to gravity is 9.8 m/s², and the mass of the block is given as 4.0 kg, the weight of the block is weight = 4.0 kg * 9.8 m/s²
= 39.2 N.
Since the force acting on the cart is equal to the weight of the block, the acceleration of the cart can be calculated using the equation force = mass * acceleration.
Plugging in the values, we get 39.2 N = 2.0 kg * acceleration.
Solving for acceleration, we find that the acceleration of the cart in Box 1 is 19.6 m/s².