Determining velocity for a pulley/rope system

In summary, the question involves a crewman trying to lower a 5.65-kg crate to the bottom of a 23.9-meter ravine using a pulley system. The crewman, who weighs 60.9 kg, accidentally slips on ice when the crate is 13.3 meters above the ground, causing the crate to accelerate towards the ground and the crewman to slide towards the edge of the cliff. The question asks for the speed at which the crate and crewman will hit the ground, assuming the ice is perfectly slick and the rope is long enough to allow the crate to hit the ground before the crewman slides over the edge. The relevant equations involve Newton's Second Law and one-dimensional kinematics.
  • #1
Katatatat
1
0
The Question:
Using a simply pulley/rope system, a crewman on an Arctic expedition is trying to lower a 5.65-kg crate to the bottom of a steep ravine of height 23.9 meters. The 60.9-kg crewman is walking along holding the rope, being careful to lower the crate at a constant speed of 1.50 m/s. Unfortunately, when the crate reaches a point 13.3 meters above the ground, the crewman steps on a slick patch of ice and slips. The crate immediately accelerates toward the ground, dragging the hapless crewman across the ice and toward the edge of the cliff.

If we assume the ice is perfectly slick (that is, no friction between the crewman and the ice once he slips and falls down), at what speed will the crate hit the ground? Assume also that the rope is long enough to allow the crate to hit the ground before the crewman slides over the side of the cliff. At what speed will the crewman hit the bottom of the ravine?​
The Relevant Equations:
F = ma
Equations for one-dimensional kinematics​
The Attempt:
I've looked at the forces for the crewman and crate separately with free-body diagrams, applying Newton's Second Law and using the following formulas to solve for acceleration, although I'm not entirely sure that is correct:
T - m1g = m1a
m2g - T = m2a​
As for the kinematics portion of the question, I assume the crate will follow a simple one-dimensional formula, while the crewman will have a projectile motion.​
 
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  • #2
Welcome to PF;
The equations are not correct. There are 3 forces on the crewman.
Which direction does the crewman's weight act?

As for the kinematics... don't assume: the problem tells you what sort of motion to expect.
 

Related to Determining velocity for a pulley/rope system

1. How do you determine the velocity of a pulley/rope system?

The velocity of a pulley/rope system can be determined by dividing the distance travelled by the time it took to travel that distance. This can be calculated by measuring the distance between the starting and ending points of the system and dividing it by the time it took for the object to move between those points.

2. What factors can affect the velocity of a pulley/rope system?

Several factors can affect the velocity of a pulley/rope system, including the weight of the object being pulled, the tension in the rope, the friction between the rope and pulley, and the angle at which the rope is being pulled. These factors can either increase or decrease the overall velocity of the system.

3. How does the number of pulleys affect the velocity of a pulley/rope system?

The number of pulleys in a system can affect the velocity in two ways. First, a single pulley system will have a lower velocity compared to a multiple-pulley system due to the increased friction and tension in the rope. Secondly, the more pulleys there are in a system, the greater the mechanical advantage, resulting in a higher velocity as less effort is required to move the object.

4. Can the velocity of a pulley/rope system be increased?

Yes, the velocity of a pulley/rope system can be increased by reducing the friction between the rope and pulley, increasing the tension in the rope, or using a larger pulley. However, it is important to note that the velocity of the system cannot exceed the speed of the object being pulled.

5. How accurate is the velocity measurement in a pulley/rope system?

The accuracy of the velocity measurement in a pulley/rope system depends on the precision of the measuring tools used and the skill of the person taking the measurements. It is important to use precise tools and take multiple measurements to ensure an accurate velocity calculation.

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