The elastic potential energy stored in the stretched spring is 1 J.
<h3>What is Hooke's law?</h3>
Hooke's law states that; provided the elastic limit is not exceeded, the extension of the spring is directly proportional to the force on the spring.
Given that;
Force on the spring = 350 Newton
Distance stretched = 7 centimeters or 0.07 m
Hence;
F = ke
k = F/e = 350 Newton/0.07 m = 5000 N/m
Work done in stretching a spring = 1/2ke^2
= 0.5 × 5000 × (2 × 10^-2)^2 =1 J
Learn more about elastic potential energy: brainly.com/question/156316
Answer:
20 ms¯¹
Explanation:
3. Determination of the final velocity
From the question given above, the following data were obtained:
Time (t) = 4 s
Acceleration (a) = 5 ms¯²
Initial velocity (u) = 0 ms¯¹
Final velocity (v) =?
Acceleration is simply defined as the change in velocity per unit time.
Mathematically, it can be expressed as:
Acceleration (a) = final velocity – Initial velocity / time
a = v – u / t
With the above formula, we can obtain the final velocity of the car as follow:
Time (t) = 4 s
Acceleration (a) = 5 ms¯²
Initial velocity (u) = 0 ms¯¹
Final velocity (v) =?
a = v – u / t
5 = v – 0 / 4
5 = v / 4
Cross multiply
v = 5 × 4
v = 20 ms¯¹
Thus, the final velocity of the car is 20 ms¯¹
The statement about pointwise convergence follows because C is a complete metric space. If fn → f uniformly on S, then |fn(z) − fm(z)| ≤ |fn(z) − f(z)| + |f(z) − fm(z)|, hence {fn} is uniformly Cauchy. Conversely, if {fn} is uniformly Cauchy, it is pointwise Cauchy and therefore converges pointwise to a limit function f. If |fn(z)−fm(z)| ≤ ε for all n,m ≥ N and all z ∈ S, let m → ∞ to show that |fn(z)−f(z)|≤εforn≥N andallz∈S. Thusfn →f uniformlyonS.
2. This is immediate from (2.2.7).
3. We have f′(x) = (2/x3)e−1/x2 for x ̸= 0, and f′(0) = limh→0(1/h)e−1/h2 = 0. Since f(n)(x) is of the form pn(1/x)e−1/x2 for x ̸= 0, where pn is a polynomial, an induction argument shows that f(n)(0) = 0 for all n. If g is analytic on D(0,r) and g = f on (−r,r), then by (2.2.16), g(z) =
Answer:
1.6 s
Explanation:
To find the time in which the potential difference of the inductor reaches 24V you use the following formula:
V_o: initial voltage = 60V
R: resistance = 24-Ω
L: inductance = 42H
V_L: final voltage = 24 V
You first use properties of the logarithms to get time t, next, replace the values of the parameter:
hence, after 1.6s the inductor will have a potential difference of 24V
Bergeron–Findeisen Process.
