# Find the apparent weight

• vbrasic
In summary, at the top of the bump, a 665N woman in a car traveling at 9.15m/s will experience a downwards centripetal acceleration of 8.05m/s^2 towards the center of the arc due to the car's motion. This results in a total downwards acceleration of 17.05m/s^2, causing her apparent weight to be 1156.96N. However, her apparent weight is not constant as the car goes over the hump and is only valid at the top of the hump when the car's instantaneous velocity is horizontal. A plot of all the forces applied on the woman at the top of the hump can help identify which force is the apparent weight.

## Homework Statement

A car traveling on a straight road at 9.15m/s goes over a hump in the road. The hump may be regarded as an arc of a circle of radius 10.4m. What is the apparent weight of a 665N woman in the car as she rides over the hump?

## Homework Equations

##F=ma##; ##a=v^2/r##

## The Attempt at a Solution

At the top of the bump the woman will experience a centripetal acceleration towards the center of the arc (i.e. downwards). The magnitude of this acceleration is ##v^2/r=8.05m/s^2##. The total downwards acceleration of the woman is hence ##9.8+8.05=17.05m/s^2##. Her true weight is ##665/9.8=67.86kg##. So, her apparent weight is ##67.86*17.05=1156.96N##. Does this sound correct?

Are you presseed doen in your seat at the top of a bump, or almost flying up ?

BvU said:
Are you presseed doen in your seat at the top of a bump, or almost flying up ?
Almost flying up; where is the problem in my analysis of the problem?

Where does the centripetal force come from ?

I should add that the apparent weight of the woman is not constant as the car goes over the hump. Usually one does this sort of calculation when the car is at the top of the hump and the instantaneous velocity is horizontal.

vbrasic said:
Almost flying up; where is the problem in my analysis of the problem?
The problem is your result: that the woman feels much heavier on the bump then on flat gound, instead of as if flying away.

Why you don't make a plot with all the forces applied on the women, (at the top of the hump), and then you identify which of them is the apparent weight

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