Best exercises for these topics. (have the amount of exercises, have 4 exercises for each.)
2 answers:
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Answer:
A. when the mass has a displacement of zero
Explanation:
The velocity of a mass on a spring can be calculated by using the law of conservation of energy. In fact, the total energy of the mass-spring system is equal to the sum of the elastic potential energy (U) of the spring and the kinetic energy (K) of the mass:
where
k is the spring constant
x is the displacement of the mass with respect to the equilibrium position of the spring
m is the mass
v is the velocity of the mass
Since the total energy E must remain constant, we can notice the following:
- When the displacement is zero (x=0), the velocity must be maximum, because U=0 so K is maximum
- When the displacement is maximum, the velocity must be minimum (zero), because U is maximum and K=0
Based on these observations, we can conclude that the velocity of the mass is at its maximum value when the displacement is zero, so the correct option is A.
Answer:
Explanation:
Given a square Piece whose side is 12 inches
Now square pieces are cut from each corner to make it a open box
Suppose x is the length of square piece at each corner
then
base square has a length of
Dimension of new box is
Volume
For maximum volume differentiate with respect to x we get
we get x=6 and 4 but at x=6 volume becomes zero therefore x=4 is valid