W=20 e(-kt)
A. Rearranging gives k= -(ln(w/20)/t
Substituting w= 10 and solving gives k=0.014
B. Using W=20e(-kt). After 0 hours, W=20. After 24 hours, W=14.29g. After 1 week (24x7=168h) W=1.9g
C. Rearranging gives t=-(ln(10/20)/k. Substituting w=1 and solving gives t=214 hours.
D. Differentiating gives dW/ dt = -20ke(-kt). Solving for t=100 gives dW/dt = 0.07g/h. Solving for t=1000 gives 0.0000002g/h
E. dW/dt = -20ke(-kt). But W=20e(-kt) so dW/dt = -kW
Answer:
a) 
b) 
c) 
Explanation:
Given masses:


Velocity of mass 1, 
Velocity of mass 2, 
a)
Initial momentum:



b)
magnitude of initial momentum:


From the conservation of momentum:



is the magnitude of final velocity.
Direction of final velocity will be in the direction of momentum:




c)
Vertical component of final velocity:


Answer:
44 N/m
Explanation:
The extension, e, of the spring = 2.9 m - 1.4 m = 1.5 m
The work needed to stretch a spring by <em>e</em> is given by

where <em>k</em> is spring constant.

Using the appropriate values,

Answer:
a. 3.039cm
b.magnetic field is 
Explanation:
Direction of the solenoid magnetic field is along the axis of the solenoid. and magnetic field due to the wire perpendicular to that due to the solenoid.. Magnetic field at r is given by:

Angle of net magnetic field from axial direction is given by:
,
Field due to solenoid:

Field due to wire:

Therefore, r:

Hence, the radial distance is 3.039cm
b.The magnetic field strength is given by:

Hence, the magnetic field is 
Thus, a swinging pendulum has its greatest kinetic energy and least potential energy in the vertical position, in which its speed is greatest and its height least; it has its least kinetic energy and greatest potential energy at the extremities of its swing, in which its speed is zero and its height is greatest.