Spring mechanics question easy

In summary, a block of mass 8 kg hangs from a ceiling on an ideal, massless spring with a spring constant of 65 N/m. The total length of the spring is 3.5 m. When a second block with the same mass is tied to the first with a massless string, the spring stretches an additional 1.5 m. After the second block is removed, the maximum velocity of the first block is found by solving for v in the equation kx^2/2=mv^2/2, where x is 1.5 added to the original length of the spring. The correct answer is 3.42.
  • #1
ronaldor9
92
1

Homework Statement



A block of mass m1 = 8 kg hangs from the ceiling on an ideal, massless spring with spring constant k = 65 N/m. With the block hanging on the spring, the total length of the spring is L = 3.5 m. When a second block with an identical mass of m2 = 8 kg is tied to the first with a massless string, the spring stretches an additional h0 = 1.5 m.

The string is cut so that mass m2 falls away. What is the maximum velocity of mass m1?

The Attempt at a Solution


[tex] \frac{kx^2}{2}=\frac{mv^2}{2} [/tex]
x=1.5 and solving for v gives 4.3
but the answer is 3.42?
 
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  • #2
Hi ronaldor9! :smile:
ronaldor9 said:
… With the block hanging on the spring, the total length of the spring is L = 3.5 m. When a second block with an identical mass of m2 = 8 kg is tied to the first with a massless string, the spring stretches an additional h0 = 1.5 m.

x=1.5 and solving for v gives 4.3
but the answer is 3.42?

1.5 isn't x …

you have to (find and) add on the bit of x that's already in the 3.5. :wink:
 
  • #3


Your attempt at a solution is correct, but there may be a mistake in your calculation. The correct answer for maximum velocity is indeed 3.42 m/s. You can double check your calculation to ensure that you are using the correct values for m, k, x, and v. Additionally, make sure you are converting all units to the correct form (e.g. kg to m/s^2). If you are still getting a different answer, please provide your calculations so I can help identify any errors.
 

Related to Spring mechanics question easy

1. What is a spring?

A spring is a mechanical device that is designed to store potential energy and release it in the form of kinetic energy when it is compressed or stretched.

2. How do springs work?

When a spring is compressed or stretched, it experiences a force that is proportional to the distance it is compressed or stretched. This force is known as the spring constant and is what allows the spring to store and release energy.

3. What are the different types of springs?

The three main types of springs are compression springs, extension springs, and torsion springs. Compression springs are designed to be compressed, extension springs are designed to be stretched, and torsion springs are designed to be twisted.

4. What are some common uses of springs?

Springs have a wide range of uses in various industries, including automotive, aerospace, and manufacturing. Some common uses of springs include shock absorbers, suspension systems, and door hinges.

5. How do I choose the right spring for my application?

Choosing the right spring for your application depends on several factors, including the amount of force required, the space available, and the type of motion needed. It is important to consult with a professional or refer to spring design charts to ensure the proper spring is selected for your specific needs.

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