Q & A: Mechanics and Newton

Consider a bob hanging from the ceiling of a car. Suppose it is moving with an acceleration a. It is a known fact that the bob will make an angle theta with the vertical because of the acceleration. Is this deviation because of inertia? My friend says that an object of mass ‘m’ moving with an acceleration ‘a’ experiences a force ‘ma’ opposite to its direction of motion. He says that it is called De Lambert’s principle. Does such a principle exist? Now consider another situation somewhat similar to the above mentioned situation. Suppose an elevator of mass ‘m’ is ascending with an acceleration ‘a’. The tension in the cable of the elevator increases by a factor ‘ma’. So in this case the principle that I mentioned earlier seems to working.# The moon moves around the sun because of the centripetal force provided by the gravitational pull of the earth and that is the case with the planets that move around the sun. But what is the balancing force that prevents it from following a spiral path and finally fall on the earth. Is it because of inertia by virtue of which it has a natural tendency to take straight line path? In many books there is a force called centrifugal force mentioned. Does such a force really exist or is it used just for calculation purposes?
- Amitabh (age 21)
India

Quite a few questions to answer.
1. a hanging bob in an accelerating car will make an angle backwards due to that inertia in the bob. it would travel at a constant velocity, but the tension in the string will not let it. so it is accelerated along with the car. The tension must be pulling it forward, so the string must angled backward.

2. the tension in the cable of a hanging mass in an accelerating ascending elevator is increased and can be explained by Newton's 2nd law.
SUM[forces] = ma
Tension - weight = ma (tension points up, weight down)
Tension = weight + ma

3. First off, lets not talk about centripetal forces. The moon would orbit the sun even if the earth weren't here. The Earth's garvity just makes the moon do a second orbit around the Earth, as both orbit the Sun.

Let's look at just one of these orbits at a time. the only force that acts on the moon or another satellite is gravity from the earth (in this simple situation). what keeps the moon from falling straight into the earth is the fact that it has a velocity. an acceleration is defined as a change in velocity with time. velocity is a vector so it has both a magnitude and direction. so a change in either of its parts will mean it is accelerating. the size of the velocity is not changing, but its direction is since it is moving in a circle. so the acceleration is not a linear one, but what we call a centripetal acceleration. so using the 2nd law again we can write:
SUM[forces] = ma
GMm/R^2 = m*a_centripetal (centripetal because the moon moves in a circle and not in or out.)
so the centripetal acceleration is just the result of all the forces, it is not the cause.

James

(published on 10/22/2007)