A five kg box is pulled along a frictionless surface by a string just capable of suspending a 15 kg mass at rest. What is the maximum acceleration that can be given to the box?
To find the maximum acceleration that can be given to the box, we need to consider the relationship between the force applied to the box and the mass of the box.
First, let's determine the maximum force that can be applied to the box. The maximum force is equal to the weight of the suspended mass, which is given as 15 kg. The weight is calculated by multiplying the mass (15 kg) by the acceleration due to gravity (9.8 m/s^2):
Weight = mass × acceleration due to gravity
Weight = 15 kg × 9.8 m/s^2
Weight = 147 N
Since the string is just capable of suspending the 15 kg mass at rest, the maximum force that can be applied to the box is also 147 N.
Next, we need to determine the acceleration of the box. To do this, we'll use Newton's second law of motion, which states that the force applied to an object is equal to the product of its mass and acceleration:
Force = mass × acceleration
In this case, the force applied to the box is the maximum force, which is 147 N, and the mass of the box is 5 kg:
147 N = 5 kg × acceleration
Rearranging the equation to solve for acceleration:
acceleration = 147 N / 5 kg
acceleration ≈ 29.4 m/s^2
Therefore, the maximum acceleration that can be given to the box is approximately 29.4 m/s^2.