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?
226N=13kg(acceleration-gravity)
gravity=9.8m/s^2
To find the minimum acceleration of the elevator, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration (F = m * a). In this case, the force applied to the block is the tension in the cord.
Given:
Mass of the block, m = 13 kg
Tension in the cord, T = 226 N
We need to find the minimum acceleration, a.
Since the cord breaks, the tension in the cord is equal to the weight of the block. The weight can be calculated using the formula W = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s²).
Weight of the block, W = m * g = 13 kg * 9.8 m/s²
Thus, the tension in the cord is equal to the weight of the block:
T = W
Now we can substitute this value of tension into Newton's second law equation:
T = m * a
226 N = 13 kg * a
To find the minimum acceleration, divide both sides of the equation by 13 kg:
a = 226 N / 13 kg
Simplifying the equation gives:
a ≈ 17.38 m/s²
Therefore, the minimum acceleration of the elevator is approximately 17.38 m/s².