Hooke's Law: Solve Work Problem at MIT East Campus Dorms

In summary, students at MIT participate in a spring semester tradition where they use surgical hose mounted on window frames to create catapults for launching balloons filled with dyed water. The hose obeys Hooke's law with a spring constant of 110 N/m. If the hose is stretched by 5.90 m and then released, the force from the hose does -649 N of work on the balloon in the pouch by the time the hose reaches its relaxed length. The elastic potential energy stored in the stretched pouch/hose is 1914.55 J, which can also be expressed as -1914.55 J of work.
  • #1
shell4987
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Homework Statement


During spring semester at MIT, residents of the parallel buildings of the East Campus dorms battle one another with large catapults that are made with surgical hose mounted on a window frame. A balloon filled with dyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room. Assume that the stretching of the hose obeys Hooke's law with a spring constant of 110 N/m. If the hose is stretched by 5.90 m and then released, how much work does the force from the hose do on the balloon in the pouch by the time the hose reaches its relaxed length?


Homework Equations


F=-kx W=Fd


The Attempt at a Solution


I tried this problem and got -649 as the answer for the force, however I feel as if it is not correct, I also don't know what to do to get work, do I just multiply the -649 by 5.9 again to get work? Am I doing something wrong?
 
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  • #2
Start by calculating the elastic potential energy stored in the streched pouch/hose.
 
  • #3
Hootenanny said:
Start by calculating the elastic potential energy stored in the streched pouch/hose.

Okay, I did that and got 1914.55 as my answer, is that my answer? It seems as if I use Ws=-1/2kx^2 the negative (-1914.55) would be my answer and work? Am I right?
 

1. What is Hooke's Law and how does it apply to work problems at MIT East Campus Dorms?

Hooke's Law is a fundamental principle in physics that describes the relationship between the force applied to an object and the resulting deformation or displacement of the object. In the context of work problems at MIT East Campus Dorms, Hooke's Law can be used to calculate the amount of work done by a force on an object, such as lifting a heavy object up the stairs.

2. How do you calculate work using Hooke's Law?

To calculate work using Hooke's Law, you need to know the force applied to an object and the displacement of the object. The equation for work is W = F * d, where W is work, F is force, and d is displacement. Hooke's Law states that the force applied to an object is directly proportional to its displacement, so you can plug in the values for force and displacement into this equation to calculate the work done.

3. What are the units of measurement for Hooke's Law?

The units of measurement for Hooke's Law depend on the specific variables being used. The force is typically measured in Newtons (N), displacement is measured in meters (m), and work is measured in Joules (J). It is important to ensure that all units are consistent when using Hooke's Law in calculations.

4. Can Hooke's Law be applied to any type of material?

Hooke's Law is generally applicable to most elastic materials, meaning materials that can be stretched or compressed and return to their original shape when the applied force is removed. However, the extent to which Hooke's Law applies to a material depends on its elasticity and the amount of force being applied. Some materials, such as rubber, may not follow Hooke's Law at all.

5. How is Hooke's Law used in engineering and science fields?

Hooke's Law is used extensively in engineering and science fields, particularly in the study of mechanics and materials. It is used to understand how objects behave under applied forces, as well as to design and analyze structures and machines. Hooke's Law is also important in fields such as geology and seismology, where it is used to study the behavior of rocks and the Earth's crust under stress.

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