Answer:
Explanation:
A direct proportionality means a linear relationship between two variables and rate of change means an application of derivatives. Hence, the mathematical model is:
If the force of gravity between a book of mass 0.50 kg and a calculator of 0.100 kg is 1.5 × 10-10 N, how far apart are they? (
1 answer:
The gravitational force between two masses m₁ and m₂ is
where
G = 6.67408 x 10⁻¹¹ m³/(kg-s²), the gravitational constant
d = distance between the masses.
Given:
F = 1.5 x 10⁻¹⁰ N
m₁ = 0.50 kg
m₂ = 0.1 kg
Therefore
1.5 x 10⁻¹⁰ N = (6.67408 x 10⁻¹¹ m³/(kg-s²))*[(0.5*0.1)/(d m)²]
d² = [(6.67408x10⁻¹¹)*(0.5*0.1)]/1.5x10⁻¹⁰
= 0.0222
d = 0.1492 m = 149.2 mm
Answer: 149.2 mm
where
G = 6.67408 x 10⁻¹¹ m³/(kg-s²), the gravitational constant
d = distance between the masses.
Given:
F = 1.5 x 10⁻¹⁰ N
m₁ = 0.50 kg
m₂ = 0.1 kg
Therefore
1.5 x 10⁻¹⁰ N = (6.67408 x 10⁻¹¹ m³/(kg-s²))*[(0.5*0.1)/(d m)²]
d² = [(6.67408x10⁻¹¹)*(0.5*0.1)]/1.5x10⁻¹⁰
= 0.0222
d = 0.1492 m = 149.2 mm
Answer: 149.2 mm
You might be interested in
Answer:
The magnitude of the magnetic force acting on the conductor is 0.75 Newton
Explanation:
The parameters given in the question are;
The length of the straight segment of wire, L = 25 cm = 0.25 m
The current carried in the wire, I = 5 A
The orientation of the wire with the magnetic field = Perpendicular
The strength of the magnetic field in which the wire is located, B = 0.60 T
The magnetic force, 'F', is given by the following formula;
F = ·L×
= I·L·B·sin(θ)
Where;
= The current flowing, I
L = The length of the wire
= The magnetic field strength, B
θ = The angle of inclination of the conductor to the magnetic field
Where I = 5 A, L = 0.25 m, B = 0.60 T, and θ = 90°, we get;
F = 5 A × 0.25 m × 0.60 T × sin(90°) = 0.75 N
Therefore
The magnitude of the magnetic force, F = 0.75 N.