Can a 2700 N Force Along r2 Free a Crate from Quicksand?

In summary: So the man will be successful in getting the crate out of the quicksand.In summary, the man trying to get the crate out of the quicksand believes that a force of 2700 N applied in the direction r2, along with a cable attached to the crate that can withstand up to 4500 N of force, will be enough to free the crate. To determine if this is true, the force produced by the mechanical crank along the r2 vector must be calculated using the properties of the dot product. Since this force is greater than the necessary 2700 N, the crate will move and the man will be successful in removing it from the quicksand.
  • #1
Peacefulchaos
3
0

Homework Statement


A crate is stuck in quicksand. The man trying to get the crate out of the quicksand thinks that a force of 2700 N applied in the direction r2 will be sufficient to get the crate free. The crate also has a cable attached to it that is connected to a mechanical crank in the direction r1. The cable can withstand up to 4500 N of force before snapping.

r1 = <400, 1200, 300> m
r2 = <-4, 8, -2> m

Will the man be successful in getting the crate out of the quicksand?


Homework Equations


unit vector = position vector / magnitude of position vector


The Attempt at a Solution



I found the unit vectors for r1 and r2, but I'm not sure what to do next. I can convert F1 and F2 to Cartesian components using the unit vectors and their magnitudes, but how can I determine if the crate moves without knowing its weight?

Thanks for any help.
 
Physics news on Phys.org
  • #2
I solved this on my own. For some reason I thought the problem was stating that F2 directed along r2 was an additional force (another force pulling it out, or something pushing from behind). It was actually saying the crank needed to produce that much force in the r2 direction, which is understandable.

So to solve this problem you would find the force that the crank produces along the r2 vector. To do this you would use the properties of the dot product. I.e., the dot product between F1 (force of crank) dot the unit vector of r2. If this is greater than the necessary 2500 N, then the crate will move (which it is).
 

What is quicksand and how does it work?

Quicksand is a mixture of fine sand, clay, and water that looks solid on the surface but actually behaves like a liquid when disturbed. When an object is placed on top of quicksand, it can sink due to the weight of the object pushing down on the sand particles and displacing the water to create a thinner, more fluid-like mixture.

How does statics play a role in a crate stuck in quicksand?

Statics is the branch of mechanics that deals with the study of objects at rest or in a state of constant motion. When a crate is stuck in quicksand, there are various forces acting on it, such as the weight of the crate, the buoyant force of the quicksand, and the friction between the crate and the quicksand. Understanding these forces and their interactions can help determine the best course of action for freeing the crate.

What factors can contribute to a crate getting stuck in quicksand?

There are several factors that can contribute to a crate getting stuck in quicksand, including the weight and size of the crate, the density and consistency of the quicksand, and the surrounding environmental conditions. For example, if the quicksand is particularly thick or deep, it may be more difficult for the crate to break free.

How can the crate be freed from the quicksand?

There are a few methods that can be used to free a crate stuck in quicksand. One option is to lighten the load of the crate by removing some of the contents or using a lever to lift it. Another method is to create a stable platform around the crate using planks or sticks to distribute the weight more evenly. It may also be possible to create a vacuum by suctioning out the water from the quicksand, allowing the crate to float to the surface.

Can quicksand be dangerous for humans?

While quicksand can be dangerous for humans, it is typically not as deadly as it is portrayed in movies and TV shows. It is possible for a person to get stuck in quicksand, but it is unlikely that they will sink all the way down. The best course of action if you find yourself stuck in quicksand is to try to stay calm, slowly move your arms and legs to create a stable platform, and call for help. It is important to avoid struggling or making sudden movements, as this can cause you to sink further into the quicksand.

Hot Threads

Recent Insights

Back
Top