The definition of work done, in some science books, is written as force x distance. This is incorrect.
The true definition is Work Done = Force x Displacement (W.D = F x s).
Suppose we move an object of mass m = 6kg (resting on the earth) against gravity g (approximately 10 m/s/s).
Let the distance moved = 20m and assume the object comes to rest 5m above the earth.
Then the total Work Done = F x s = mg x s = 6 x 10 x 5 = 300 J (joules).
Notice that this is also equal to the increase in gravitational potential energy of the object. Also note that force and displacement are vector quantities whilst work done is a scalar quantity.
Saturday, 20 July 2013
Friday, 5 July 2013
High School Science Text Books
Often when I have taught physics to high school students there has arisen conflict between what I am telling the students and what their issued text states. I just bite the bullet and point out why the text is incorrect. "Obviously" those teachers of science who rely on the text being correct may be inadvertently disadvantaging their students. Not a nice thought!
NEWTON'S SECOND LAW OF MOTION
It is most unfortunate that a significant number of teachers of science put forward Newton's Second Law as being Force = Mass x Acceleration.
If an unbalanced force acts on an object its momentum will change with time. Newton's Second Law states that the unbalanced force is directly proportional to the rate of change of momentum with time and is in the same direction as the force.
Momentum p = mv and is a vector quantity. Hence, from the above definition F = dp/dt = d(mv)/dt.
Upon expansion we get F = mdv/dt + vdm/dt. Now, dv/dt = a.
Hence, F = ma + vdm/dt. This is the correct mathematically presentation of Newton's Second Law.
If we assume that the inertial mass of the object does not change then dm/dt = 0 , and Newton's Second Law reduces to F = ma + 0 = ma.
Consider an object of mass m having an initial velocity of v'. Its momentum (p) is mv'. Suppose an unbalanced force F acts on the object for t seconds and it's new velocity is v''. Hence, its new momentum is mv''. Note, I have made the assumption that its mass has not changed. Let the change in velocity be v. Then, v = v'' - v,'
From Newton's Second Law we get F = (Change in momentum) / (Change in time).
Hence, F = (mv'' - mv')/t = m(v''-v')/t = m(v/t) = ma.
If an unbalanced force acts on an object its momentum will change with time. Newton's Second Law states that the unbalanced force is directly proportional to the rate of change of momentum with time and is in the same direction as the force.
Momentum p = mv and is a vector quantity. Hence, from the above definition F = dp/dt = d(mv)/dt.
Upon expansion we get F = mdv/dt + vdm/dt. Now, dv/dt = a.
Hence, F = ma + vdm/dt. This is the correct mathematically presentation of Newton's Second Law.
If we assume that the inertial mass of the object does not change then dm/dt = 0 , and Newton's Second Law reduces to F = ma + 0 = ma.
Consider an object of mass m having an initial velocity of v'. Its momentum (p) is mv'. Suppose an unbalanced force F acts on the object for t seconds and it's new velocity is v''. Hence, its new momentum is mv''. Note, I have made the assumption that its mass has not changed. Let the change in velocity be v. Then, v = v'' - v,'
From Newton's Second Law we get F = (Change in momentum) / (Change in time).
Hence, F = (mv'' - mv')/t = m(v''-v')/t = m(v/t) = ma.
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