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.
Wednesday, 26 June 2013
FORCE
There are numerous teachers of science who define force as a push or a pull. This is a very poor definition. The definition of force is embedded in Newton's first law of motion.
Newton's first law of motion may be stated as - Every body continues in its state of rest or of uniform motion in a straight line unless it is acted upon by an unbalanced force.
It is important to emphasise that all motion is relative. Having asked a student if she is sitting still I then ask her how many times she has been around the sun. Primary and secondary students readily pick up the concept of relative motion and frames of reference.
Uniform motion in a straight line means travelling in a straight line at a constant speed. Hence the velocity of the body is constant and therefore the acceleration is zero (a = dv/dt).
From Newton's first law an unbalanced force can do one of two things-
1. It can change a body's state of rest.
OR
2. It can change its state of uniform motion in a straight line.
Part 1 is quite straight forward. Suppose an object is at rest relative to a white board. If an unbalance force acts on the object it will now move relative to the white board.
Part 2 can be "quantized". Suppose the object is travelling in a straight line at a constant speed and an unbalanced force acts on it. Various outcomes are possible. The object-
(a). Continues moving in a straight line but changes its speed.
(b). Maintains the same speed but changes direction.
(c). Changes its speed and direction.
In all of the above cases the object changes its velocity with time and therefore must be accelerating.
It is to be noted that the definition of force is an operational definition. We do not say what a force is. Instead we say what a force can do. This concept is quite readily absorbed into the minds of attentive and motivated primary and secondary students.
Newton's first law of motion may be stated as - Every body continues in its state of rest or of uniform motion in a straight line unless it is acted upon by an unbalanced force.
It is important to emphasise that all motion is relative. Having asked a student if she is sitting still I then ask her how many times she has been around the sun. Primary and secondary students readily pick up the concept of relative motion and frames of reference.
Uniform motion in a straight line means travelling in a straight line at a constant speed. Hence the velocity of the body is constant and therefore the acceleration is zero (a = dv/dt).
From Newton's first law an unbalanced force can do one of two things-
1. It can change a body's state of rest.
OR
2. It can change its state of uniform motion in a straight line.
Part 1 is quite straight forward. Suppose an object is at rest relative to a white board. If an unbalance force acts on the object it will now move relative to the white board.
Part 2 can be "quantized". Suppose the object is travelling in a straight line at a constant speed and an unbalanced force acts on it. Various outcomes are possible. The object-
(a). Continues moving in a straight line but changes its speed.
(b). Maintains the same speed but changes direction.
(c). Changes its speed and direction.
In all of the above cases the object changes its velocity with time and therefore must be accelerating.
It is to be noted that the definition of force is an operational definition. We do not say what a force is. Instead we say what a force can do. This concept is quite readily absorbed into the minds of attentive and motivated primary and secondary students.
Monday, 17 June 2013
ACCELERATION
There are numerous teachers of science who define acceleration as being the rate of change of speed with time. This is totally incorrect. With that definition we have acceleration = change in speed divided by change in time. Before looking at the true definition of acceleration I would like to mention distance,displacement, speed and velocity.
Suppose an objects initial position in three dimensional space is (0,0,0)m.Let an unbalanced force act on the object for 10 seconds. Suppose the object travels a distance of 200 metres and its final position is (100,0,0)m. Hence, distance travelled is 200m and the objects displacement is 100m. Its average speed is (change in distance) / (change in time) = 200/10 = 20m/s. Its average velocity = (change in displacement) / (change in time) = 100/10 = 10m/s.
Speed is a scalar quantity (it has magnitude only). Velocity is a vector quantity (it has magnitude and direction).
Acceleration is properly defined as being the rate of change of velocity with time. Acceleration is a vector quantity.
Suppose an object travels for 10s in a circular path at a constant speed of 15m/s. If acceleration was defined as (change in speed) / (change in time) then the acceleration of this object would be zero. This cannot be correct. An object travelling in a circle is being acted upon by an unbalanced force (otherwise it must be stationary or travelling in a staight line at constant speed according to Newton's First Law of Motion). If the inertial mass of the object is m and its mass remains constant then the force acting on the object = mass x acceleration. Hence, it must be accelerating. As it moves in a circle its velocity keeps changing with time. Hence, again it must be accelerating.
Suppose an objects initial position in three dimensional space is (0,0,0)m.Let an unbalanced force act on the object for 10 seconds. Suppose the object travels a distance of 200 metres and its final position is (100,0,0)m. Hence, distance travelled is 200m and the objects displacement is 100m. Its average speed is (change in distance) / (change in time) = 200/10 = 20m/s. Its average velocity = (change in displacement) / (change in time) = 100/10 = 10m/s.
Speed is a scalar quantity (it has magnitude only). Velocity is a vector quantity (it has magnitude and direction).
Acceleration is properly defined as being the rate of change of velocity with time. Acceleration is a vector quantity.
Suppose an object travels for 10s in a circular path at a constant speed of 15m/s. If acceleration was defined as (change in speed) / (change in time) then the acceleration of this object would be zero. This cannot be correct. An object travelling in a circle is being acted upon by an unbalanced force (otherwise it must be stationary or travelling in a staight line at constant speed according to Newton's First Law of Motion). If the inertial mass of the object is m and its mass remains constant then the force acting on the object = mass x acceleration. Hence, it must be accelerating. As it moves in a circle its velocity keeps changing with time. Hence, again it must be accelerating.
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