I have difficulties doing some explanatory questions, which I am not sure how to support the following events:
Explain the following with ref to Newton's Laws and the forces involved.
(a) A woman at the equator weights herself daily on a bathroom scale. Suppose that the earth rotates 3x faster, will the reading change?
(b) The moon does not fall towards teh earth although it is udner the pull of earth's gravity.
For each of the following scenarios, state and explain whether the object in motion requires a maximumor minimum speed to maintain its motion in a circle
(a) A car going over a hump (a circular arc) - It should be minimum speed but dont know how to explain...
(b) water in a apil being swung in a verrtical circle (hmmm, minimum speed at the top and max speed at the bottom?)
(c) A bus negotiating a circular bend on the road (not very sure about this one.)
Sorry i know this is quite a number of questions to be answered but i need help in doing such conceptual questions. thanks all
(a) A woman at the equator weights herself daily on a bathroom scale. Suppose that the earth rotates 3x faster, will the reading change?
Yes, it will change. If the Earth rotates faster, it means that the woman requires more centripetal force. Bathroom scales measure the reaction force. If we draw the free body diagram of the woman, mg - R = resultant force = mv^2/r
Hence, R = mg - mv^2/r .
If it rotates 3 times as fast, mv^2/r will be larger, and hence R will be smaller.
(b) The moon does not fall towards the earth although it is udner the pull of earth's gravity.
The Earth's gravitational force is used for accelerating towards the Earth's centre constantly, resulting in a circular orbit by the Moon.
(a) A car going over a hump (a circular arc) - It should be minimum speed but dont know how to explain...
Requires maximum speed. You don't see cars travelling slowly being unable to clear a hump right?
Too fast a speed, you will need a larger centripetal force. If the weight of the car is insufficient to supply the required centripetal force, the car will fly and lose contact with the hump
(b) water in a pail being swung in a verrtical circle (hmmm, minimum speed at the top and max speed at the bottom?)
No, you need a minimum speed at the bottom and top of the circle.
If the speed is too slow, at the top of the circular motion, the water will fall out of the pail.
If fast enough, the pail will exert a force on the water for the circular motion, and by N3L, the water will exert an equal but opposite force on the pail, and hence it won't fall out.
(c) A bus negotiating a circular bend on the road (not very sure about this one.)
Maximum speed required.
If too fast, it might topple. Think of the times you took a bus.
and if you still can't picture the moon's rotation, just imagine yourself throwing a ball parallel to the ground that you can see. it will fall in an arc towards the ground, right? then imagine yourself throwing the ball again and again, faster and faster. you will create a bigger and bigger arc, right? assuming you have incredibly strength, there will come a point in time where the ball's trajectory is supposed to fall to the ground, but instead it is at the same height above the ground from where you threw it with the same initial speed. so the ball would just be going round the earth.