Final answer:
To find the minimum time to raise a bucket without breaking the cord, calculate the gravitational force on the bucket and then use the relationship between work, power, and time. The work done lifting the bucket is compared against the power generated without exceeding the cord's tension limit to determine the minimum time.
Step-by-step explanation:
The question refers to the minimum time required to raise a 5.60 kg bucket of water a vertical distance of 13.0 m without breaking the cord with a breaking strength of 85.0 N. First, we must recognize the maximum allowable force is the tension the cord can support. The only forces acting on the bucket are gravity and the tension from the cord, and since the bucket must be lifted at a constant speed, this means the maximum tension (85.0 N) will equal the gravitational force on the bucket. The gravitational force is the mass of the bucket multiplied by the acceleration due to gravity (9.8 m/s2).
We calculate the force due to gravity on the bucket (Fgravity) as Fgravity = mass × gravity = 5.60 kg × 9.8 m/s2 = 54.88 N. The bucket can be lifted at a constant velocity as the tension is more than the gravitational force, so we don't need to take into account the extra force to overcome inertia (because we're dealing with a case of constant speed, not acceleration). The power generated should be at its maximum just below the breaking point of the cord.
Our next step is to find the power output using the formula for power (P = F × v, where F is force and v is velocity). To keep the tension below the breaking point, we use a force equal to the breaking strength minus the force of gravity: P = (85.0 N - 54.88 N) × v. With constant power, we can find the minimum velocity (v) using the desired power output. However, since power does not directly relate to time, we need to use the relationship between work done (W = Force × distance) and power (P = W/t) to find the time (t). Work done will be the gravitational force times the distance lifted (W = 54.88 N × 13.0 m).
Calculating the work gives us 713.44 J (joules). To find the time we can rearrange the power equation to t = W/P and use the maximum power just below the breaking strength as calculated above. To avoid overstressing the cord, we use slightly less power than the breaking limit would allow, hence we have t = 713.44 J / P. With the power limit, we ensure that the tension never exceeds 85.0 N. You would then have to calculate the required time for each provided answer option (A, B, C, D) to determine which one is realistic without surpassing the cord's breaking strength.