Please write your homework neatly. Don't try to cram all the problems into the
minimum space. Show your work clearly, and useful diagrams are always appropriate
and may get extra points. You may work with others, but the work should be your
own. I expect numeric answers to have a reasonable number of significant figures
and proper units.
Note: WebAssign grades only on the answer; I will grade only (mostly) on the
method! Make your method clear.
1. The net force on a cart is determined to have the following dependence
on position:
F(x) = Ax + Bx3 with A = -5 and B = 0.08.
(a) Assuming that x is in meters and F is in N, what are the units
of A and B?
(b) Find the work done by this force as it acts on the cart that moves from
x = 1.00 m to x = 2.00 m.
(c) If the cart has a mass of 3.00 kg and an initial speed at x = 1.00 m of
2.50 m/s, find the speed of the cart at x = 2.00 m.
| 2. Two identical springs are shown, with unstretched lengths L = 40 cm. A mass m = 2.5 kg is attached and I hold it in the position shown where the springs are relaxed. I release the mass and it falls to its lowest position h = 30 cm below the starting position. Determine the spring constant of the springs. | |
[Hint: the "x" in the potential energy for the spring
is the difference between the stretched and unstretched lengths of the spring.]
| 3. A block of mass m is initially pushed against a
spring of constant k, compressing the spring by an amount x0. The spring
and mass are on an incline of theta to the horizontal, and there is no friction.
When you release the block it moves up the incline and eventually leaves
the spring (they are not connected). (a) Find an expression for the speed of the block when it leaves the spring. |
 |
(b) Find an expression for the position where the block has moved
a maximum distance up the incline.
(c) If I do not compress the spring enough initially, the mass will not leave
the spring. Find an expression for the threshold initial compression, x0,
for which this occurs.
Expressions may contain no other symbols than m, k, x0,
theta, and g.
CAVEAT: The "x" in the expression for spring potential energy, and the "y" in the expression for gravitational potential energy are not perpendicular to each other.
4. (a) How does the integral for work differ from the integral for impulse?
List as many ways as you can.
(b) How are the two intergrals alike?
This page maintained by Anne G. Young. Last modified 27-Oct-2004 .