# Change in Acceleration: Analyzing Force Time Curve

• david smith
In summary, the force plate measures the force exerted by an object based on its mass and acceleration due to gravity. When the object is displaced vertically, there will be a change in the measured force. This change can be represented by a force-time curve, which can indicate either a change in acceleration or velocity. However, due to the constant mass, the curve actually represents a change in acceleration over time.
david smith
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If I stand on a force plate it will measure a force in Newtons equivalent to my mass X acceleration due to Gravity, let's say that is 1000N. If I displace the mass vertically (and I'm only interested in force normal to the force plate) then there will be a change in the force applied.

Again if I roll across the force plate on a roller skate then a force is applied and the force /time curve characterised will be flat because there is no displacement of the mass vertically.

So my question is if there is always an acceleration due to gravity then does the acceleration due to vertical displacement of the mass represent a change in acceleration or a change in velocity. Which is the more correct term?

This change in acceleration or velocity can be characterised on a computer screen as a force time curve. As the mass is constant then the curve actually represents a change in acceleration. If the curve were a straight line slope then this would be a change in velocity i.e.
acceleration but as the line is curved then this represents a change of acceleration over time.

Is this correct?

Cheers Dave Smith

The force plate will measure the force, which will be mass times acceleration. If there is no change in velocity there will be no acceleration and no change in measured force. Imagine an arrangement which consists of a crane, also mounted on the force plate. If the crane is lifting the mass at a steady speed, the force plate will record the same value as when the mass is hanging, stationary, on the crane. Whilst starting or stopping, however, there will be a change in 'apparent weight' - i.e. force on the plate.

Yes, your understanding is correct. The change in acceleration observed in the force time curve represents a change in the rate at which an object's velocity is changing. This can be caused by various factors, such as a change in the applied force or a change in the object's mass. In the case of your example, the change in acceleration is due to the vertical displacement of the mass, which results in a change in the force applied to it. This change in acceleration can be accurately captured and analyzed through the force time curve.

## 1. What is acceleration?

Acceleration is the rate of change of an object's velocity over time. It is a vector quantity, meaning it has both magnitude and direction. In simpler terms, acceleration is how fast an object's speed is changing.

## 2. How is acceleration related to force?

According to Newton's Second Law of Motion, acceleration is directly proportional to the net force acting on an object and inversely proportional to its mass. This means that the greater the force applied to an object, the greater its acceleration will be. Similarly, the more massive an object, the less it will accelerate for a given force.

## 3. What is a force-time curve?

A force-time curve is a graph that shows the applied force on an object over a period of time. It is commonly used to analyze the change in acceleration of an object, as the slope of the curve represents the acceleration at any given point. The area under the curve also represents the impulse, or change in momentum, of the object.

## 4. How can analyzing a force-time curve help us understand changes in acceleration?

By examining the slope and shape of a force-time curve, we can determine the magnitude and direction of acceleration of an object. Steeper slopes indicate larger accelerations, while flat areas indicate no acceleration. Changes in the shape of the curve can also indicate changes in the direction or magnitude of the applied force, which can affect the acceleration of the object.

## 5. What factors can affect a force-time curve?

The shape and slope of a force-time curve can be influenced by various factors, such as the mass and initial velocity of the object, the type and direction of the applied force, and any external forces acting on the object (such as friction or air resistance). The shape of the object itself can also affect the force-time curve, as objects with different shapes and surface areas will experience different levels of air resistance.

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