Calculating Mass of Bucket to Descend 9.144m in 4s

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In summary, the conversation discusses a scenario where a man on a cliff is about to jump onto a rope connected to a massless bucket on the ground. The man wants to descend 9.144m in 4 seconds and the question asks how much weight needs to be put into the bucket for this to happen. By using the equation d=0.5at^2, the acceleration of the man is found to be 1.143m/s^2. Then, by using the equation m1a1=m2a2, the mass of the bucket is calculated to be 72.14kg. The conversation confirms that this solution is correct.
  • #1
UrbanXrisis
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There is a pully with a rope though it. The rope of the left side is on the ground connected to a massless bucket. The right side has a man on a cliff about to jump on the rope. The man wants to descend 9.144m in exactly 4s. The question asks how much weight to put into the massless bucket for the man to descend 9.144m in exactly 4s. There isn't any inital velocity.

So, I need to find the acceleration of the man:
d=.5at^2
9.144m=.5(a)4^s
a=1.143m/s^2

Now I will find how much the mass of the bucket has to be:
m1a1=m2a2
m1(9.81)=(81.65kg)(9.81-1.143)
m=72.14kg

is this correct?
 
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  • #2
Im taking it that the problem said the man weights 81.65kg, right?
 
  • #3
yes, forgot to say that
 
  • #4
Seems correct 2 me, good job. :smile:
 

What is the formula for calculating the mass of a bucket to descend 9.144m in 4s?

The formula for calculating the mass of a bucket to descend 9.144m in 4s can be derived from the equations of motion, specifically the formula for displacement:
Displacement = Initial Velocity * Time + (Acceleration * Time^2)/2.
In this case, the bucket is starting from rest, so the initial velocity is 0 m/s. The displacement is given as 9.144m and the time is 4s. Therefore, the formula becomes:
9.144m = (Acceleration * 4s^2)/2.
Rearranging for acceleration, we get:
Acceleration = 9.144m / (4s^2)/2 = 4.572m/s^2.
Now, using the formula F=ma, where F is the force (weight) acting on the bucket, m is the mass of the bucket, and a is the acceleration, we can calculate the mass of the bucket as:
Mass (m) = Force (F) / Acceleration (a) = Weight (mg) / Acceleration (a) = 9.8kg * 4.572m/s^2 = 44.856kg.

What is the significance of calculating the mass of the bucket to descend 9.144m in 4s?

Calculating the mass of the bucket to descend 9.144m in 4s can be useful in various scenarios. For example, if you are designing a pulley system to lift the bucket, knowing the mass of the bucket can help you determine the amount of force needed to lift it. Also, in an experiment or project involving the bucket, knowing its mass can provide important data for analysis and interpretation. Additionally, this calculation can also be used to ensure the safety and stability of the bucket and the system it is being used in.

How can the calculation of the mass of the bucket to descend 9.144m in 4s be applied to real-life situations?

The calculation of the mass of the bucket to descend 9.144m in 4s can be applied to various real-life situations. For example, it can be used in the construction of elevators or cranes to determine the weight capacity and ensure the safety of the system. It can also be used in amusement park rides to calculate the mass of passengers and ensure the ride is balanced and safe. This calculation can also be applied in physics experiments to study the effects of gravity and acceleration on different masses.

What are the assumptions made in the calculation of the mass of the bucket to descend 9.144m in 4s?

The calculation of the mass of the bucket to descend 9.144m in 4s is based on certain assumptions. These include assuming that the acceleration due to gravity is constant (9.8m/s^2) and that there is no air resistance or friction acting on the bucket. Additionally, the calculation assumes that the bucket starts from rest and moves in a straight line with constant acceleration throughout the entire 4 seconds.

What are some possible sources of error in the calculation of the mass of the bucket to descend 9.144m in 4s?

There are a few potential sources of error in the calculation of the mass of the bucket to descend 9.144m in 4s. These include measurement errors, such as inaccuracies in measuring the time or displacement, as well as uncertainties in the value of acceleration due to gravity (9.8m/s^2). Additionally, environmental factors such as air resistance or friction can affect the acceleration of the bucket and introduce errors in the calculation. It is important to consider and minimize these sources of error for a more accurate calculation of the mass of the bucket.

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