asst 9

course Phy 121

HcCԕassignment #009

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

009. Forces exerted by gravity

Physics I

06-26-2007

......!!!!!!!!...................................

11:46:15

`q001. Note that there are 10 questions in this set.

.You have done the Introductory Force Experiment in which you used rubber bands and bags of water, and you understand that, at least in the vicinity of the Earth's surface, gravity exerts downward forces. You have also seen that forces can be measured in units called Newtons. However you were not given the meaning and definition of the Newton as a unit of force. You are also probably aware that mass is often measured in kilograms.

Here we are going to develop in terms of an experiment the meaning of the Newton as a force unit. Suppose that a cart contains 25 equal masses. The cart is equal in mass to the combined total of the 25 masses, as indicated by balancing them at equal distances from a fulcrum. The cart is placed on a slight downward incline and a weight hanger is attached to the cart by a light string and suspended over a low-friction pulley at the end of the ramp. The incline is adjusted until the cart, when given a slight push in the direction of the hanging weight, is observed to move with unchanging, or constant, velocity (and therefore zero acceleration).

The masses are then moved one at a time from the cart to the hanger, so that the system can be accelerated first by the action of gravity on one of the masses, then by the action of gravity onto of the masses, etc.. The time required for the system to accelerate from rest through a chosen displacement is observed with one, two, three, four, five, ... ten of the masses.

The acceleration of the system is then determined from these data, and the acceleration is graphed vs. the proportion of the total mass of the system which is suspended over the pulley. It is noted that if the entire mass of the system, including the cart, is placed on the weight hanger, there will be no mass left on the incline and the entire weight will fall freely under the acceleration of gravity.

Suppose the data points obtained for the 5 of the first 10 trials were (.04, 48 cm/s^2), (.08, 85 cm/s^2), (.12, 125 cm/s^2), (.16, 171 cm/s^2), (.20, 190 cm/s^2). Sketch these points on an accurate graph of acceleration vs. proportion of weight suspended and determine the slope and y-intercept of the line. What is your slope and what is the y intercept? What is the equation of the line?

......!!!!!!!!...................................

RESPONSE -->

the slope is the rise over run so going by the first two points it is 925

the y intercept looks to be about 25cm/s^2

confidence assessment: 2

.................................................

......!!!!!!!!...................................

11:47:35

`q002. Do the points seem to be randomly scattered around the straight line or does there seem to be some nonlinearity in your results?

......!!!!!!!!...................................

RESPONSE -->

they seem to be close to the straight line

confidence assessment: 3

.................................................

......!!!!!!!!...................................

11:47:56

`q003. If the acceleration of the system is indeed proportional to the net force on the system, then your straight line should come close to the origin of your coordinate system. Is this the case?

......!!!!!!!!...................................

RESPONSE -->

yes, it is

confidence assessment: 3

.................................................

......!!!!!!!!...................................

11:49:13

`q003. What is it that causes the system to accelerate more when a greater proportion of the mass is suspended?

......!!!!!!!!...................................

RESPONSE -->

the acceleration of gravity causes it to accelerate more

confidence assessment: 2

.................................................

......!!!!!!!!...................................

11:51:39

`q004. This results of this sort of experiment, done with good precision, support the contention that for a given mass the acceleration of a system is indeed proportional to the net force exerted on the system. Other experiments can be done using rubber bands, springs, fans and other nongravitational sources of force, to further confirm this result.

In another sort of experiment, we can see how much force is required on different masses to obtain a certain fixed acceleration. In such experiments we find for example that if the mass is doubled, it requires twice the force to achieve the same acceleration, and that in general the force required to achieve a given acceleration is proportional to the amount of mass being accelerated.

In a certain experiment using the same cart and masses as before, plus several additional identical carts, a single cart is accelerated by a single suspended mass and found to accelerate at 18 cm/s^2. Then a second cart is placed on top of the first and the two carts are accelerated by two suspended masses, achieving an acceleration of 20 cm / s^2. Then a third cart is placed on top of the first to and the three carts are accelerated by three suspended masses, achieving and acceleration of 19 cm/s^2. A fourth cart and a fourth suspended mass are added and an acceleration of 18 cm/s^2 is obtained. Adding a fifth cart in the fifth suspended mass an acceleration of 19 cm/s^2 is obtained. All these accelerations are rounded to the nearest cm/s^2, and all measurements are subject to small but significant errors in measurement.

How well do these results indicate that to achieve a given acceleration the amount of force necessary is in fact proportional to the amount of mass being accelerated?

......!!!!!!!!...................................

RESPONSE -->

all of the acceleration measurements were within experimental error, so the results support the proportionality hypothesis

confidence assessment: 3

.................................................

......!!!!!!!!...................................

11:53:11

`q005. Now we note again that the force of gravity acts on the entire mass of the system when an entire system is simply released into free fall, and that this force results in an acceleration of 9.8 m/s^2. If we want our force unit to have the property that 1 force unit acting on 1 mass unit results in an acceleration of 1 m/s^2, then how many force units does gravity exert on one mass unit?

......!!!!!!!!...................................

RESPONSE -->

gravity would exert about 10 force units on one mass unit

confidence assessment: 1

.................................................

......!!!!!!!!...................................

11:54:25

`q006. If we call the force unit that accelerates 1 mass unit at 1 m/s^2 the Newton, then how many Newtons of force does gravity exert on one mass unit?

......!!!!!!!!...................................

RESPONSE -->

gravity exerts 9.8 newtons of force on one mass unit

confidence assessment: 1

.................................................

......!!!!!!!!...................................

11:54:53

`q007. The mass unit used here is the kilogram. How many Newtons of force does gravity exert on a 1 kg mass?

......!!!!!!!!...................................

RESPONSE -->

9.8 kg

confidence assessment: 1

.................................................

......!!!!!!!!...................................

11:55:41

`q008. How much force would gravity exert on a mass of 8 kg?

......!!!!!!!!...................................

RESPONSE -->

gravity would exert 78.4 Newtons on a mass of 8 kg

confidence assessment: 3

.................................................

......!!!!!!!!...................................

11:56:49

`q009. How much force would be required to accelerate a mass of 5 kg at 4 m/s^2?

......!!!!!!!!...................................

RESPONSE -->

it would take 9.8 * 5 Newtons, i'm not sure how to factor in the 4 m/s^2

confidence assessment: 1

.................................................

......!!!!!!!!...................................

11:58:04

`q010. How much force would be required to accelerate the 1200 kg automobile at a rate of 2 m/s^2?

......!!!!!!!!...................................

RESPONSE -->

1200 kg * 2

2400 Newtons

confidence assessment: 3

.................................................

"

Good work. Looks like you got everything here.