# Dynamics: Minimum Force Problem

• JM92
In summary, the conversation was about finding the smallest value for the mass M in a system with a coefficient of static friction of 0.100. The equations used were Fnet = ma, ∑F(Horizontal) = 0, ∑F(Vertical) = 0, Ff = μ・FN, Fgx = Fg・sinθ, and Fgy = Fg・cosθ. The correct answer was 4.98kg and the mistake was drawing Ff in the wrong place.
JM92
Hi, nice to meet everybody here at physicsforums.com! I'm JM92 and I have a physics problem I need help with.

## Homework Statement

Find the smallest value of the mass M for which the system will remain at rest given that the coefficient of static friction is 0.100
[PLAIN]http://img695.imageshack.us/img695/6328/physics2.jpg

## Homework Equations

Fnet = ma
∑F(Horizontal) = 0
∑F(Vertical) = 0

Ff = μ・FN
Fgx = Fg・sinθ
Fgy = Fg・cosθ

## The Attempt at a Solution

[PLAIN]http://img3.imageshack.us/img3/4139/physics11.jpg
I retyped and redrew everything with MS paint.. Hopefully that made it easier to read and not harder..

PS. The correct answer is 4.98kg.

EDIT: Sorry, the thread title should be called "Minimum Mass Problem"

Last edited by a moderator:
You've drawn Ff in the wrong place. M is the mass of the second block; if it is any smaller, the first block will slide down the incline.

How small can M be?

vertigo said:
You've drawn Ff in the wrong place. M is the mass of the second block; if it is any smaller, the first block will slide down the incline.

How small can M be?

Ohh! I was looking at it backwards, then. With Ff in the opposite direction, I got the correct answer. Thank you very much!

## 1. What is the minimum force problem in dynamics?

The minimum force problem in dynamics refers to finding the minimum amount of force required to move an object from one position to another in a given amount of time. This problem is important in understanding the motion of objects and the forces acting upon them.

## 2. How is the minimum force problem solved?

The minimum force problem is typically solved using principles of mechanics and Newton's laws of motion. This involves setting up equations of motion and using mathematical techniques such as calculus to determine the minimum force required.

## 3. What factors influence the minimum force required?

The minimum force required is influenced by several factors, including the mass of the object, the distance it needs to be moved, and the time frame in which it needs to be moved. Additionally, external forces such as friction and air resistance can also affect the minimum force required.

## 4. How does the minimum force problem relate to real-world situations?

The minimum force problem is applicable in many real-world situations, such as designing efficient machines and structures, determining the optimal force required for a specific task, and understanding the motion of objects in various scenarios. It is also important in fields such as engineering, physics, and biomechanics.

## 5. What are the limitations of the minimum force problem?

The minimum force problem assumes ideal conditions and does not take into account factors such as variability in external forces, changes in the object's mass, and the effects of non-uniform motion. It also does not consider the effects of human error or limitations in measurement accuracy. Furthermore, the minimum force required may not always be achievable due to practical limitations.

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