The first man-made satellite, Sputnik 1, was launched into space in 1957. This satellite was used to study the conditions found
2 answers:
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Answer:
3.258 m/s
Explanation:
k = Spring constant = 263 N/m (Assumed, as it is not given)
x = Displacement of spring = 0.7 m (Assumed, as it is not given)
= Coefficient of friction = 0.4
Energy stored in spring is given by
As the energy in the system is conserved we have
The speed of the 8 kg block just before collision is 3.258 m/s
(a) 907.5 N/m
The force applied to the spring is equal to the weight of the object suspended on it, so:
The spring obeys Hook's law:
where k is the spring constant and is the stretching of the spring. Since we know
, we can re-arrange the equation to find the spring constant:
(b) 1.45 cm
In this second case, the force applied to the spring will be different, since the weight of the new object is different:
So, by applying Hook's law again, we can find the new stretching of the spring (using the value of the spring constant that we found in the previous part):
(c) 3.5 J
The amount of work that must be done to stretch the string by a distance is equal to the elastic potential energy stored by the spring, given by:
Substituting k=907.5 N/m and , we find the amount of work that must be done:
Answer:
E ≈ 1.70 10⁵ N/C
Explanation:
The electric field is a vector quantity, so we can calculate the field of each plate and then add them. To calculate the field of a plate let's use Gauss's law
Φ = ∫ E. dA = / ε₀
To apply this law we must create a Gaussian surface that takes advantage of the symmetry of the problem. The electric field lines on the surface are perpendicular, so the Gaussian surface that will be a cylinder with the base parallel to the plate.
On this surface the normal to the base (A) is parallel to the field lines whereby the scalar product is reduced to the ordinary product. The normal on the sides of the cylinder is perpendicular to the field, therefore, the product scale is zero.
∫I E dA = /ε₀
Let's look for the load under the cylinder, let's use the concept of load density
σ = / A
= σ A
Let's write Gauss's law for this case
E A = /ε₀
E A = σ A / ε₀
E = σ / ε₀
As the field is emitted for each side of the plate the value to only one side is
E = G / 2ε₀
This expression is the same for each plate, now let's add the electric field at the requested point
R = (0.50, 0.00, 0.00) cm
We see that this point is on the X axis, between the plates that are at the points y = -1.0 cm and y = 1.0 cm, as the plates are very large the test point is between them
The negative plate has an incoming field and the positive plate has an outgoing field, the test load is always positive. The field due to the negative plate goes to the left, the field through the positive plate goes to the left at this point whereby two are added
E = E_ + E +
E = σ1 / 2ε₀ + σ2 / 2ε₀
E = 1 / 2o (σ1 + σ2)
Let's calculate the value
E = 1/2 8.85 10⁻¹² (1.00 10⁻⁶ + 2.00 10⁻⁶)
E = 3 10⁻⁶ / 17.7 10⁻¹²
E = 1,695 10⁵ N / C
E ≈ 1.70 10⁵ N/C