The required spring constant:
The spring constant of the spring is 
.
Calculation:
The mass of the car is m=1200 kg, the speed of the car is v=25 m/s, and after colliding the spring is brought to rest at a distance of x=2.5m. Let the spring constant of the spring is, k.
From the conservation of energy,
Total initial kinetic energy= Total final potential energy of the spring
Therefore,
Now, substituting the values of the mass of the car, speed of the car, and displacement, we get:
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Answer: 33.5 x 10⁻⁶ C
Explanation:
By definition, the capacitance is the relationship between the charge on one of the plates (assuming it's a capacitor) and the voltage between them:
C = Q / V
Now, it can be showed that we can find the capacitance of a parallel-plate capacitor, taking into account the geometry and the dielectric material only, as follows:
C = ε A /d = ε₀ εr A / d
If the dielectric is air, we can assume εr = 1
If the space between plates is filled with a dielectric of dielectric constant 7.74, the new value for capacitance (regarding the former value) must be 7.74 times larger, as A and d didn't change.
So, in order to produce the same potential difference between the plates, we need to increase the charge, exactly 7.7 times:
Q = 7.7. 4.33 . 10⁻⁶ C = 33.5 . 10⁻⁶ C
The electric force on the proton is:
F = Eq
F = electric force, E = electric field strength, q = proton charge
The gravitational force on the proton is:
F = mg
F = gravitational force, m = proton mass, g = gravitational acceleration
Since the electric force and gravitational force balance each other out, set their magnitudes equal to each other:
Eq = mg
Given values:
q = 1.60×10⁻¹⁹C, m = 1.67×10⁻²⁷kg, g = 9.81m/s²
Plug in and solve for E:
E(1.60×10⁻¹⁹) = 1.67×10⁻²⁷(9.81)
E = 1.02×10⁻⁷N/C
Answer:
all the forces occur in pairs that if one object exerts a force on another object, then the second object exerts an equal and opposite reaction force on the first.
Θ is the angular displacement = ωt
ω is the angular velocity = θ/t
α is the angular acceleration = ω/t
