If the work done to stretch an ideal spring by 4.0 cm is 6.0J, what is the spring constant (force constant) of this spring?
2 answers:
As AL2006 correctly pointed out the formula is 1/2 kx^2. I was thinking of force and work is the integral of force over the distance applied. So now
and
and
Answer:
Spring constant or the force constant, k = 7500 N/m.
Explanation:
Given that,
Energy stored in the spring, E = 6 J
Stretching in the spring, x = 4 cm = 0.04 m
To find,
The spring constant (force constant) of this spring.
Solution,
We know that the work done by the spring when it is stretched is given by :
k is the spring constant
k = 7500 N/m
So, the spring constant (force constant) of this spring is 7500 N/m.
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Answer:
Explanation:
For parallel inductors ,
For series combination
Total inductance
= 16.67 + 20
= 36.67 mH .
reactance of total inductance at 300 kHz
= ω where ω is angular frequency
= 2πf
= 2 x 3.14 x 300 x 10³ x 36.67 x 10⁻³
= 69.1 x 10³ ohm
Total rms current = Vrms / reactance
= 60 / 69.1 x 10³ A
= .87 x 10⁻³ A
= .87 mA
Answer:
a)
a = 2 [m/s^2]
b)
a = 1.6 [m/s^2]
c)
xt = 2100 [m]
Explanation:
In order to solve this problem we must use kinematics equations. But first we must identify what kind of movement is being studied.
a)
When the car moves from rest to 40 [m/s] by 20 [s], it has a uniformly accelerated movement, in this way we can calculate the acceleration by means of the following equation:
where:
Vf = final velocity = 40 [m/s]
Vi = initial velocity = 0 (starting from rest)
a = acceleration [m/s^2]
t = time = 20 [s]
40 = 0 + (a*20)
a = 2 [m/s^2]
The distance can be calculates as follows:
where:
x1 = distance [m]
40^2 = 0 + (2*2*x1)
x1 = 400 [m]
Now the car maintains its speed of 40 [m/s] for 30 seconds, we must calculate the distance x2 by means of the following equation, it is important to emphasize that this movement is at a constant speed.
v = x2/t2
where:
x2 = distance [m]
t2 = 30 [s]
x2 = 40*30
x2 = 1200 [m]
b)
Immediately after a change of speed occurs, such that the previous final speed becomes the initial speed, the new Final speed corresponds to zero, since the car stops completely.
Note: the negative sign of the equation means that the car is stopping, i.e. slowing down.
0 = 40 - (a *25)
a = 40/25
a = 1.6 [m/s^2]
The distance can be calculates as follows:
0 = (40^2) - (2*1.6*x3)
x3 = 500 [m]
c)
Now we sum all the distances calculated:
xt = x1 + x2 + x3
xt = 400 + 1200 + 500
xt = 2100 [m]