# How to solve a Sum of Forces Problem with Two Springs and Varied Masses?

• simplemail1
In summary, the problem statement is asking for the maximum amplitude of the oscillation, given the spring's initial position and the spring constant.
simplemail1
1. The problem statement, all variables and given/known

## Homework Statement

There is a spring with two crates, (5kg +3 kg) as shown in this picture. (1)
The spring constant is 1000 n/m.

I need to find
a) How much the spring is compressed from its initial position (at rest)
b) The frequency of the oscillation
c) Max amplitude after contact

And then there is a different spring, oscillating horizontally with 2 boxes on top of each other, m1 on m2. The maximum force of friction is define as f.

I need to find the a) max horizontal acceleration for the m1 not to slip on m2 and I need to find the b) max amplitude for simple harmonic motion without m1 slipping. I'm not given any numbers whatsoever.

## The Attempt at a Solution

For a) I would think I would do (8)(9.8) and then do that against the force of the constant
b) I think I would use w (frequency?) = (k/m)^1/2.
c) I'm not too sure on this

I don't know what to do afterwards (or at all) for the second spring

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Any advice to kick me off?

Hi simplemail1,

For part a of the first problem, you can definitely use the sum of the forces; however, the acceleration is not zero so you would need to be able to tell what the acceleration is and set the sum of the forces equal to $ma$. As an alternative, I would try using conservation of energy to find the answer.

Hi,

Exactly, all of these questions can be solved from the Newton's equation F=ma.
a) In this case, the equilibrium position is asked, so a=0 and sum of forces=0. In the sum of forces, you have the gravitation force mg and the reaction of the spring k(l-l0). In those kind of problems always be aware of the difference between the position at rest and the natural length of the spring l0 that are different due to the gravitation
b) F=ma allows you to obtain the differential equation of movement, mx''+kx=0 so you can have the pulsation
c) solving the differential equation allows you to have x(t), x'(t) and x''(t), which all will be sinusoidal functions... It is easy to have their maximum

For the second spring, always the same problem, but the forces will be different: no gravitation, but friction force.

Hi jonpoux,

jonpoux said:
Hi,

Exactly, all of these questions can be solved from the Newton's equation F=ma.
a) In this case, the equilibrium position is asked, so a=0 and sum of forces=0. In the sum of forces, you have the gravitation force mg and the reaction of the spring k(l-l0). In those kind of problems always be aware of the difference between the position at rest and the natural length of the spring l0 that are different due to the gravitation

The wording of the question is not too clear, but I don't think they are asking for the equilibrium position in this problem. They are setting up an oscillation so I think they want the maximum distance the spring is compressed from it's initial position during the oscillation.

simplemail,

It doesn't look like you typed in the complete statement of the problem. It might be best if you type in everything the problem said; little details can make a big difference.

## 1. What is the Sum of Forces Problem?

The sum of forces problem is a concept in physics that involves calculating the total force acting on an object. This is done by adding up all the individual forces acting on the object, taking into account their direction and magnitude.

## 2. How do I solve a Sum of Forces Problem?

To solve a sum of forces problem, you must first identify all the forces acting on the object and determine their direction and magnitude. Then, use vector addition to add up all the forces and find the resultant force. Finally, use Newton's second law of motion (F=ma) to calculate the acceleration of the object.

## 3. What is the difference between balanced and unbalanced forces?

In a sum of forces problem, balanced forces refer to a situation where the net force on an object is zero, meaning that all the forces acting on the object cancel each other out. Unbalanced forces, on the other hand, result in a nonzero net force and cause the object to accelerate in the direction of the resultant force.

## 4. Can the Sum of Forces Problem be applied to real-life situations?

Yes, the sum of forces problem is applicable to real-life situations and is commonly used in engineering, sports, and other fields. For example, in a car accident, the forces acting on the car can be calculated to determine the impact and potential damage.

## 5. What are some common mistakes when solving Sum of Forces Problems?

One common mistake is forgetting to include all the forces acting on the object. It is important to consider all forces, including gravity, friction, and applied forces. Another mistake is not properly considering the direction of forces, which can result in incorrect calculations. It is also important to use the correct units and pay attention to sign conventions when adding forces.

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