class 051012

Find

• the work done by the gravitational force on the system
• the work done by the system against the gravitational force
• the work done by the frictional force acting on the system
• the work done by the system against the frictional force
• the change in KE

of a system consisting of a domino block of mass 30 grams as it coasts 50 cm down an incline on which the frictional force is .1 Newton, and on which the change in its vertical coordinate has magnitude 20 cm.

Find the same if the domino block coasts 50 cm up the incline.

If the block coasting down the incline starts with velocity 0 then what is its final velocity on the incline?

The the block coasting up the incline starts with velocity 7 m/s then what will be its velocity after coasting the 50 cm?

Friction exerts a force of .1 N in the direction opposite the motion.  Choosing downward as the positive direction, the displacement for the domino moving down the incline is +.50 m and the force exerted by friction is -.1 N, so the work done by friction ON the system is -.1 N * .50 m = -.05 J.

Gravity acts in the vertical downward direction, and only displacement in this direction contributes to the work done by gravity.  Using downward as positive the force of gravity is .030 kg * 9.8 m/s^2 = .29 N, or approximately .3 N.  Using the approximate value with the downward displacement of 20 cm we get

• work done by gravity ON system = .20 m * .3 N = .06 N.

Since `dPE is the work done BY the system against gravity, `dPE = -.06 J.

The following two statements are equivalent:

• Negative work done by friction on the system tends to slow it down, to decrease its KE. 
• Positive work done by the system against friction tends to slow it down, decrease its KE.

The following two statements are also equivalent:

• Negative work done by gravity on the system tends to slow it down, to decrease its KE. 
• Positive work done by the gravity on the system tends to slow it down, decrease its KE.

The work done by friction ON the system is -.05 J.

The work done ON the system by gravity is +.06 J.

• Positive work done on the system tends to increase KE.
• Negative work done on the system tends to decrease KE.

We have -.05 J being done by friction and +.06 J done by gravity, so the net work in +.01 J.

So KE increases by .01 J.

The system does .05 J of work against friction.  That is, .05 J of work is done BY the system against friction.

The system does -.06 J of work against gravity.  That is, work against gravity BY the system is -.06 J.  This is the PE change of the system.  Remember, `dPE is defined as the work done BY the system AGAINST a conservative force.  (This is why we have to think about the difference between work done ON and work done BY the system.  Our intuition wants to think in terms of the forces exerted by gravity ON a system, but the PE concept requires us to also consider the work done BY the system against gravity).

So we can say that the PE of the system changes by -.06 J, which will tend to increase the KE.  The system also does .05 J of work against the nonconservative frictional force.

Using the equation

`dPE + `dKE + `dW_noncons_by = 0 we see that

-.06 J + `dKE + .05 J = 0.

We could write the equation in terms of `dW_noncons_on insteadh of `dW_noncons_by.

`dPE + `dKE - `dW_noncons_on = 0, which can be written as

`dW_noncons_on = `dPE + `dKE.

Note that _by or _on means BY the system or ON the system.  The by or on that counts modifies the word system.