When you weigh yourself, how does the support force of the scale acting on you compare to the gravitational force between you an
d Earth?
1 answer:
Answer with explanation:
We know that when we weigh ourselves on a scale the scale measures the Reaction force that acts between the scale and the person who wishes to determine his weight.
The free body diagram of the person on a weighing scale is represented in the attached figure.
As we can see for equilibrium
where,
R is the reaction force between the support and the person
W is the weight of the person which by definition is the force that the earth exerts on the person.
Thus according to the above relation we conclude that that support force of the scale is equal to the gravitational force in magnitude but is opposite in direction.
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We have the relation
where denotes the velocity of a body A relative to another body B; here I use B for boat, E for Earth, and R for river.
We're given speeds
Let's assume the river flows South-to-North, so that
and let be the angle made by the boat relative to East (i.e. -90° corresponds to due South, 0° to due East, and +90° to due North), so that
Then the velocity of the boat relative to the Earth is
The crossing is 153.0 m wide, so that for some time we have
which is minimized when so the crossing takes the minimum 30.0 s when the boat is pointing due East.
It follows that
The boat's position at time
is
so that after 30.0 s, the boat's final position on the other side of the river is
and the boat would have traveled a total distance of
