# Proving that apparent weight is 5 times actual weight (no numbers)

• testme
In summary, to find the apparent weight of a motorcycle, you would need to consider its bottom most position, calculate the resultant force, and divide by 5 to find the speed required.
testme

## Homework Statement

Without numbers, identify how you could find the apparent weight of motorcycle to be 5 times that of the actual weight. The motorcycle is going up a loop the loop with a velocity of v.

Fnet = mv^2/r
Fg = mg

## The Attempt at a Solution

Fnet = mv^2/r
Fg + Fn = mv^2/r
Fn = mv^2/r - Fg
Fn = mv^2/r - mg
Fn = mv^2/r - mgr/r
Fn = (mv^2 - mgr)/r

I have no idea of this is right or if I'm completely misinterpreting the question.

This seems to be an open ended question and does not require you to consider a specific position for the bike.May I suggest that you consider the bike at its bottom most position(that's where its apparent weight will be biggest for a constant speed).What are the two relevant forces on the bike,in what directions do they act and what is an expression for the resultant force?

hi testme!
testme said:
Without numbers, identify how you could find the apparent weight of motorcycle to be 5 times that of the actual weight. The motorcycle is going up a loop the loop with a velocity of v.

I have no idea of this is right or if I'm completely misinterpreting the question.

they're asking for an explanation in words

start by deciding:

at which point in the loop is the apparent weight greatest?

Thats what I was assuming. The bike was at the bottom, the two forces acting upon it are the normal force (apparent weight) and the gravitational force (actual weight).

using that I came up with the equation

Fnet = mv^2/r
Fg + Fn = mv^2/r
Fn = mv^2/r - Fg
Fn = mv^2/r - mg
Fn = mv^2/r - mgr/r
Fn = (mv^2 - mgr)/r

Though I'm not sure if that'd be the right way to find out. Also, that value would have to be 5 times your mass times gravitational acceleration.

When the questions asks without numbers they mean as in no numbers given, so just theoretically the process. That's what my teacher said.

At the bottom the normal force(apparent weight) acts upwards and the weight acts downwards.

words only:

"as soon as it goes into the loop, if will have a centripetal acceleration which can only be supplied by an increased normal force, which (for fixed v) will be proportional to … , which can be made large enough by making … sufficiently … "

Fnet = mv^2/r
-Fg + Fn = mv^2/r
Fn = mv^2/r + Fg
Fn = mv^2/r + mg
Fn = mv^2/r + mgr/r
Fn = (mv^2 + mgr)/r

Would that be it then?

Looks good but remember Fn=5mg

Would it be fine that we find Fn using that and then we multiply Fg we would find by 5 at the very end?

Fg is the "true weight" of the bike and that remains constant.What you are finding is an equation giving the necessary speed(v) for a given radius r for the bike to have an "apparent weight"(at the bottom) of 5mg.

I get that, but what I mean is does it matter if I divide Fn by 5 at the end or multiply Fg by 5? Could I just say 5Fg must equal Fn or Fn/5 must equal Fg for this to be true?

I'm not sure that I understand you.At the bottom the resultant force is Fn-mg.
(Fn represents the apparent weight in other words the weight that would be measured,by say,a set of scales over which the bike rides).
We can write: Fn-mg=mv^2/r
If the apparent weight is to be 5 times the real weight then Fn=5mg so we can write:
5mg-mg=4mg=mv^2/r

Nevermind, I got my answer, thanks for the help!

## 1. What is apparent weight and how is it different from actual weight?

Apparent weight refers to the perceived weight of an object, while actual weight refers to the true measurement of the object's mass. Apparent weight may differ from actual weight due to external forces such as gravity or buoyancy.

## 2. How can one prove that apparent weight is 5 times actual weight without using numbers?

One way to prove this is through the use of a scale and a known weight, such as a standard 1kg weight. By placing the known weight on the scale and measuring its apparent weight, then placing the object in question on the scale and measuring its apparent weight, one can compare the two values and determine if the apparent weight is indeed 5 times the actual weight.

## 3. What factors can affect the apparent weight of an object?

External forces such as gravity, buoyancy, and air resistance can affect the apparent weight of an object. Additionally, the surface on which the object is placed and the precision of the measurement tools can also impact the apparent weight.

## 4. Can apparent weight ever be greater than actual weight?

Yes, apparent weight can be greater than actual weight if the external forces acting on the object are greater than its own weight. For example, if an object is placed in water and the buoyant force is greater than the object's weight, the apparent weight will be greater than the actual weight.

## 5. How can understanding apparent weight be useful in scientific research?

Understanding apparent weight can be useful in experiments and research involving gravity, buoyancy, and other external forces. It can also help in understanding the behavior of objects in different environments and can aid in the design of structures and equipment that need to withstand varying forces.

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