liang81077  Date: Tuesday, 05.28.2019, 4:47 AM  Message # 1 
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Added (05.28.2019, 4:48 AM)  The result we got from the experiment is that as the total mass of the tub increases, the shorter the distance that it slides along the floor. Why is this so? Let’s assume that there are two tubs with different weights in them and find out the reason why the heavier tub travels a shorter distance than the lighter tub.
There are three stages in moving the tub with a rubber band. The first stage is when the rubber band hasn’t been released and is pulled back, the second stage when the rubber band is released and is going back to its original straight position, the third stage is when the rubber band is straight and the tub is going forward on its own.
In the first stage, the only energy is the elastic potential energy in the rubber bands. Elastic potential energy (measured in the unit joules) is equal to ½ multiplied by the stretch length ("x") squared, multiplied by the spring constant "k." As the stretch length of the rubber band in the experiment is a fixed value and the spring constant is also fixed as we are using the same rubber band, the elastic potential energy before the release of the rubber band is always the same no matter what the mass of the tub in front of it is. As a result, we can have this equation: P1 = P2, where P1 and P2 are the elastic potential energy of the rubber bands with tubs of different masses in front of them.
In the second stage, the rubber band is released and is going back to its original straight position. In this stage, the potential energy of the rubber bands is transferring into two energy: the kinetic energy of the tub and the work done by friction between the tub and the floor. How does the mass of the tub affect the work done by friction? The equation to calculate the work done by friction is f × d, the frictional force times the distance the object travels. The distance the tub, heavy or light, travels when the rubber band went from a pulledback position to a straight line is a fixed value. The frictional force is calculated the equation F = μmg, which means that the mass of the tub is directly proportional to the friction between the tub and the floor. So the heavier of the two tubs is going to have more friction than the less heavy tub as it has more mass. As the distance the two tubs travel in stage 2 is fixed and the heavier tub has a larger frictional force, the work done by the friction of the heavier tub is larger than of the lighter tub. To find the relationship between the kinetic energy of the two tubs, we can have the following equations:∵ P1 = P2, ∴ K1 + W1 = K2 + W2, where K1 and W1 are the kinetic energy and the work done by the friction of the lighter tub and K2 and W2 are of the heavier tub. As W1 < W2, K1 > K2.
Added (05.28.2019, 4:48 AM)  In the third stage, after the rubber band is straight and the tub is going forward on its own, there is no more potential energy transferring into kinetic energy, so the only forces left are the kinetic energy of the tub and the work done by the frictional force. The tub keeps sliding until all of its kinetic energy is transferred to the work done by friction. The kinetic energy of the lighter tub K1 is transferred to the work done by friction W3, and the kinetic energy of the heavier tub K2 is transferred to W3. ∵ K1 > K2, ∴W3 > W4. The work done by friction is calculated by multiplying friction with the distance an object travels. W3 = f1 × d1 and W4 = f2 × d2. By rearranging the equation, we can have d1 =W3f1and d2 =W4f2. As mentioned before, W3 > W4 and f1 < f2, we get the final result, d1 > d2, the distance the lighter tub travels is longer than the distance the heavier tub travels.


 
liangcx126  Date: Wednesday, 05.29.2019, 2:06 AM  Message # 2 
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 Why can't we solve it with F = ma, like, the heavier the mass, the lower the acceleration.


 
liang81077  Date: Wednesday, 05.29.2019, 2:09 AM  Message # 3 
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 Well you only know that F is a constant, and the mass. So you will only be able to know the acceleration. The formula to get distance from acceleration is 1/2 at^2. However, you are not able to know the speed because you did not time the experiment. Also, the force is not constant because the force is different at different stages of the rubber band. Therefore you have to use energy to calculate.


 
liangcx126  Date: Wednesday, 05.29.2019, 12:38 PM  Message # 4 
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 But you can use your logic to think about it, the greater the acceleration, the higher the speed that it will reach, and the further that it would travel. ;)


 
liangcx126  Date: Thursday, 05.30.2019, 11:05 AM  Message # 5 
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 @liang81077 It isn't d1 =W3f1and d2 =W4f2, it is d1=w3 over f1 and d2=w4 over f2


 
liang81077  Date: Thursday, 05.30.2019, 11:07 AM  Message # 6 
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 Quote liangcx126 ( ) @liang81077It isn't d1 =W3f1and d2 =W4f2, it is d1=w3 over f1 and d2=w4 over f2 kk


 