Ball rolling down a hill again
Let us calculate how long it will take a basketball to roll down a hill of height 5m and
incline 30. Suppose the ball has a mass 0.5kg, and radius R = 10cm. We already did this
problem last lecture, but now well do it with t
Impulse-momentum equation
We have now studied N2L, and the WE equation. Another equivalent approach,
derivable from N2L, and particularly useful when the forces are time-dependent, is the
impulse-momentum equation.
Impulse
First lets talk about impulse. T
Generalization of WE equation to cover rotation
So our WE equation remains,
But now we include the fact that work can be done by torques according to the equation
above,
and that if an object is rotating, it has an additional KE of:
Example
If the disk is
Bungee cords
Suppose that you want to jump off of a bridge 200m high bridge with a bungee cord tied
to your waist. You want the cord length to be such that you come to rest just above the
ground. If the spring constant of the cord is k = 500N/m, how long
Measuring the height of a hill or roller coaster
Suppose youre driving along a road, perhaps 8th avenue, and you want to measure the
height of the hill there. You can do this in your car in the following way. Put the car in
neutral at the top. Suppose you
Power
Sometimes were interested in the rate at which work is done, i.e. the power, not the
amount of work itself. For instance, horsepower (Hp) is a measure of the rate at which
work can be done. Looking at it another way, we may be interested in the rate
The Work-Energy equation applied to rotation
All of our uses of the Work-Energy equation so far have applied only to translation. But
we will remedy this now, and look at how it applies to rotation.
Work performed by arbitrary torque
When we first started
Using the Impulse-momentum equation on systems of objects
When dealing with a system of objects, instead of splitting up the objects piece by piece,
we can use the impulse-momentum equation on them as a whole. This is similar to what
we did with N2L when
Skating on hill when fall off?
Consider you start at the top of a semi-circular hill and roll down with your skateboard
(well approximate you as a ball). If the hill is 10m high, at what height will you fall off
the hill, i.e., when will you lose contact
Pushing shopping cart with a variable force
Consider the same example as above, but this time, let our force change with position.
Suppose that in the beginning it takes a little while (3m) for our force to get up to its
maximum value, and then we get tir