Particle dropped on platform with spring - Compression of springs

In summary, the purpose of dropping a particle on a platform with a spring is to observe the compression of the spring and understand the relationship between force and compression. The mass of the particle affects the compression of the spring, and other factors such as height, stiffness, and external forces can also influence it. The compression of the spring can be measured using a ruler or measuring tape. This experiment has real-life applications in studying shock absorbers, trampolines, and designing and testing springs in engineering.
  • #1
rasa
1
0
A massless platform is kept on a light elastic spring.
When a particle of mass 100g is dropped on the platform from a hieght of 24cm it strikes the platform and compresses the spring by 1cm.
From what hieght should the particle be dropped to cause a compression of 4cm?
[text book answer: 396cm]
 
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  • #2
Use the fact that energy (kinetic + potential) is conserved.
 
  • #3


Based on the given information, we can use the equation for potential energy to solve for the initial height of the particle. The potential energy at the point of release is equal to the potential energy at the point of impact (assuming no energy is lost to other factors such as air resistance). We can set up the equation as follows:

mgh = kx

Where m is the mass of the particle (0.100 kg), g is the acceleration due to gravity (9.8 m/s^2), h is the initial height, k is the spring constant, and x is the compression distance (0.04 m).

Solving for h, we get:

h = (kx)/mg

Since the spring constant and the mass of the particle are given, we can plug in the values and solve for h:

h = [(2.5 N/m)(0.04 m)]/(0.100 kg)(9.8 m/s^2)

h = 0.102 m

Therefore, the particle should be dropped from a height of 102 cm (or 1.02 m) to cause a compression of 4 cm. This is equivalent to 396 cm as given in the textbook answer.
 

Related to Particle dropped on platform with spring - Compression of springs

1. What is the purpose of dropping a particle on a platform with a spring?

The purpose of this experiment is to observe the compression of the spring when a particle is dropped on the platform. This can help us understand the relationship between the force applied on the spring and its resulting compression.

2. How does the mass of the particle affect the compression of the spring?

The mass of the particle affects the compression of the spring because the greater the mass, the more force is applied on the spring when it is dropped onto the platform. This results in a larger compression of the spring compared to when a lighter particle is used.

3. What factors can influence the compression of the spring in this experiment?

The factors that can influence the compression of the spring include the mass of the particle, the height from which it is dropped, the stiffness of the spring, and external forces such as air resistance.

4. How can we measure the compression of the spring in this experiment?

The compression of the spring can be measured by using a ruler or a measuring tape to determine the distance between the original position of the spring and its compressed position after the particle is dropped on the platform.

5. What are some real-life applications of this experiment?

This experiment can be applied in various real-life scenarios, such as studying the impact of a falling object on a spring-based shock absorber in a car, or understanding the behavior of a trampoline when someone jumps on it. It can also be used in engineering to design and test springs for different purposes.

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