The cable supporting a 2150-kg elevator has a maximum strength of 2.2×104 N .
What maximum upward acceleration can it give the elevator without breaking?
2.2*10^4 = mg + ma =2150(9.81+a)
To determine the maximum upward acceleration the cable can provide without breaking, we need to consider the tension in the cable.
The tension in the cable is equal to the weight of the elevator plus the force required to accelerate it upward. In equation form, this can be written as:
Tension = Weight + Force
The weight of the elevator can be calculated using the formula:
Weight = mass × acceleration due to gravity
The acceleration due to gravity can be considered approximately 9.8 m/s².
Therefore, the weight of the elevator is given by:
Weight = 2150 kg × 9.8 m/s²
Next, we rearrange the equation to solve for the force required to accelerate the elevator upward:
Force = Tension - Weight
Using the given maximum strength of the cable, which is 2.2×10^4 N, we can substitute the values into the equation:
Force = 2.2×10^4 N - Weight
Finally, since we want to find the maximum upward acceleration, we can rearrange the equation F = ma to solve for acceleration:
Acceleration = Force / mass
Substituting the values into the equation:
Acceleration = (2.2×10^4 N - Weight) / 2150 kg
By calculating this expression, you can find the maximum upward acceleration that the cable can provide without breaking.