0.17 Phy1150: force and motion -- units of force  (Page 9/9)

This situation is considerably more complicated and will definitely require some calculations.The tension labeled R goes to zero immediately, but the tensions labeled P and Q do not go to zero.

Movement

None of the masses remain in equilibrium. Mass A starts falling toward the floor, dragging Mass Band Mass C horizontally toward the pulley.

The driving force

Once again, the only force causing all three masses to move is the weight of Mass A (49.05 newtons), which has not changed. However,that force is now trying to move a total of 10 kg instead of only 5 kg or 7 kg as in the two scenarios described above.

A force of 49.05 newtons is not sufficient to cause a mass of 10 kg to accelerate at 9.81 m/s^2. Instead, the acceleration of each mass is proportional to the force and inversely proportional to the total mass.

a = f/m = (49.05*newtons)/(10*kg)

Entering the rightmost expression into the Google search box and pressing Enter tells us that

a = 4.9 m / s^2

Half the acceleration of gravity

Note that this is half the acceleration of gravity. This makes sense, because the force attributable to gravitational attraction acting on a mass of 5 kg isbeing applied to 10 kg of mass. It follows, therefore, that the acceleration that is achieved will be only half the acceleration of gravity.

What is the value of tension P?

Tension P is exerting a horizontal force on the right side of Mass B that is causing that mass and Mass C to accelerate at 4.9 m / s^2. The force required to achieve that acceleration on a mass of5 kg is

P = m*a = 5*kg*4.9 m / s^2

Once again using the Google calculator, we learn that

P = 24.5 newtons

Mass B and Mass C together represent 50-percent of the total mass, and tension P is 50-percent of the force applied to the total mass.

What is the value of tension Q?

Tension Q is exerting a horizontal force on the right side of Mass C that is causing Mass C to accelerate at 4.9 m / s^2. The force required to achieve that acceleration on a mass of3 kg is

Q = m*a = 3*kg*4.9 m / s^2

Once again using the Google calculator, we learn that

Q = 14.7 newtons

Mass C is 30-percent of the total mass, and tension Q is 30-percent of the force applied to the total mass.

Do the calculations

I encourage you to repeat the calculations that I have presented in this lesson to confirm that you get the same results. Experiment withthe scenarios, making changes, and observing the results of your changes. Make certain that you can explain why your changes behave as they do.

Resources

I will publish a module containing consolidated links to resources on my Connexions web page and will update and add to the list as additional modulesin this collection are published.

Miscellaneous

This section contains a variety of miscellaneous information.

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