A person in an elevator is holding a 13 kg block by a cord rated to withstand a tension of 226 N. When the elevator starts up, the cord breaks. What was the minimum acceleration of the elevator?
To find the minimum acceleration of the elevator, we need to analyze the forces acting on the block just before the cord breaks.
Let's consider the forces acting on the block:
1. The force of gravity acting downward, given by the mass (m) of the block multiplied by the acceleration due to gravity (g ≈ 9.8 m/s²). So, the force of gravity (Fg) = m * g.
2. The tension force (T) exerted by the cord pulling the block upward.
When the cord breaks, the tension force becomes zero, and only the force of gravity acts on the block.
Now, let's use the formula for Newton's second law of motion to solve for the minimum acceleration (a) of the elevator:
ΣF = m * a
Since we're interested in the minimum acceleration, we'll consider the forces just before the cord breaks. Thus, the only force acting on the block is the force of gravity. So, we have:
Fg = m * a
Now, substitute the values provided:
Fg = 13 kg * 9.8 m/s² (gravitational acceleration)
Therefore, the minimum acceleration of the elevator is:
a = Fg / m = (13 kg * 9.8 m/s²) / 13 kg
Simplifying, we find:
a = 9.8 m/s²
Thus, the minimum acceleration of the elevator is 9.8 m/s².