Weight on a Scale Down an Incline vs. True Weight

In summary, the problem involves Judy coasting down an incline on a skateboard with spring scales attached to measure her weight. The scales will indicate 3/4 of her true weight due to the force of gravity being split between the normal force and the component parallel to the incline. Friction is necessary between Judy and the scales to prevent her from sliding off and to produce a reading on the scales.
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Weight on a Scale Down an Incline vs. True Weight

Homework Statement


Judy fastened a set of bathroom spring scales to a wedge shaped skate board as shown and coasted freely down a 30 degree slope. The wheels were well oiled and the platform supporting the scales was horizontal. What fraction of her true weight was indicated by the scales?
Why would there need to be a force of friction between Judy and the scales?


Homework Equations


Fg = mg


The Attempt at a Solution


(Pictures in attachments)

Fg = mg
Fg_|_ = mgsin60º

FN = Fg _|_
FN = mgsin60º

FNy = FNcos30º
FNy = mgsin60ºcos30º
FNy = (3/4)mg

The weight will be 3/4 the true weight. (I think)


I'm not too sure why there will have to be friction between Judy and the scale. Will the scale accelerate downwards and she will slip off if there's no friction? Will the scale read zero?
 

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  • #2
Your reasoning (and perhaps your trig) is a bit unclear. Try this: What's the acceleration of the woman?
 

1. What is the difference between weight on a scale down an incline and true weight?

Weight on a scale down an incline is the measurement of an object's weight when placed on a scale that is not perpendicular to the ground. This measurement may be different from the object's true weight, which is the force of gravity acting on the object.

2. Why does the weight on a scale down an incline differ from the true weight?

The weight on a scale down an incline is affected by the angle of the incline. As the incline becomes steeper, the scale will measure a lower weight due to the component of the object's weight that is acting parallel to the incline. This means that the scale is not measuring the object's true weight, which is always perpendicular to the ground.

3. How can the true weight of an object be calculated when on an incline?

To calculate the true weight of an object on an incline, you can use trigonometry. The force of gravity acting on the object can be split into two components: the perpendicular component (true weight) and the parallel component (weight on the scale). By using the angle of the incline, you can calculate the true weight using the formula W = Ws / cosθ, where Ws is the weight on the scale and θ is the angle of the incline.

4. What factors can affect the weight on a scale down an incline?

The weight on a scale down an incline can be affected by the angle of the incline, the surface friction between the object and the incline, and the accuracy and precision of the scale itself. Additionally, the weight on the scale will be affected by the distribution of the object's mass and any external forces acting on the object.

5. How does the weight on a scale down an incline affect the accuracy of measurements?

If the angle of the incline is not taken into account, the weight on a scale down an incline can lead to inaccurate measurements. This is because the scale is measuring a component of the object's weight, rather than the true weight. To ensure accurate measurements, the angle of the incline must be considered and the true weight of the object should be calculated using trigonometry.

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