A person in an elevator is holding a 15 kg block by a cord rated to withstand a tension of 180 N. When the elevator starts up, the cord breaks. What was the magnitude of the minimum acceleration of the elevator?
To determine the magnitude of the minimum acceleration of the elevator, we need to analyze the forces acting on the block when the cord breaks.
Let's assume the upward acceleration of the elevator is denoted as "a". In this situation, the only force acting on the block is its weight, which is given by the equation:
Weight = mass x acceleration due to gravity (g)
Given that the mass of the block is 15 kg, the weight can be calculated as:
Weight = 15 kg x 9.8 m/s^2
Weight = 147 N
So, when the cord breaks, the weight of the block (147 N) will be the only force acting on it.
Since the cord is rated to withstand a tension of 180 N, which is greater than the weight of the block, the cord breaking implies that the upward force exerted on the block is less than its weight. Therefore, the net force acting on the block will be:
Net Force = Weight - Upward Force
Net Force = 147 N - Upward Force
Since the only force acting on the block is its weight, we can rewrite the equation as:
Net Force = Weight - weight
Net Force = 0
According to Newton's second law of motion, the net force is equal to mass times acceleration (F = m * a). Since the net force is zero, we can conclude that the acceleration of the block in this situation is also zero.
Therefore, the magnitude of the minimum acceleration of the elevator is 0 m/s^2.