Solving the Plunge: Investigating Falling Pliers in the Amazon

[element41]

Homework Statement

A biologist working 80 meters high in the Amazon tree canopy drops her pliers used for crimping
bands on animal legs.

1) Assuming the pliers hit nothing on the way to the ground, how fast will the pliers be moving when
they reach the ground?


2) When the pliers hit the forest floor, they come to a stop in 0.05 seconds. What force does the ground
exert on the 400 gram pliers?




3) How deep do the pliers sink into the ground when they come to a stop?

Homework Equations

I don't know what equations to use.

The Attempt at a Solution

i need maybe a guide line on how to do this problem.


Thank you

 

[rock.freak667]

Consider conservation of energy

 

[kerimek]

for your question. I would first start by gathering all the necessary information, such as the height of the drop (80 meters), the mass of the pliers (400 grams), and the time it takes to come to a stop (0.05 seconds). From there, I would use the basic equation for calculating the final velocity of an object in free fall: vf = √(vi^2 + 2ad), where vf is the final velocity, vi is the initial velocity (which in this case is 0 since the pliers were dropped), a is the acceleration due to gravity (9.8 m/s^2), and d is the distance (in this case, the height of the drop).

Using this equation, we can calculate that the pliers will be moving at a final velocity of approximately 39.2 m/s when they reach the ground.

To calculate the force exerted by the ground on the pliers, we can use Newton's second law of motion, which states that force (F) equals mass (m) multiplied by acceleration (a): F = ma. In this case, the mass of the pliers is 0.4 kg and the acceleration is -9.8 m/s^2 (since the pliers are slowing down when they hit the ground). Therefore, the force exerted by the ground on the pliers is approximately 3.92 Newtons.

To determine how deep the pliers will sink into the ground, we can use the equation for calculating the distance an object travels under constant acceleration: d = (vi^2 + vf^2)/2a. In this case, vi and vf are both 0, and a is still -9.8 m/s^2. Plugging in these values, we can calculate that the pliers will sink approximately 10.1 centimeters into the ground.

I hope this helps guide you in solving the problem. Remember to always gather all the necessary information and use the appropriate equations to solve the problem. Good luck!