Answer:
The options are not shown, so let's derive the relationship.
For an object that is at a height H above the ground, and is not moving, the potential energy will be:
U = m*g*H
where m is the mass of the object, and g is the gravitational acceleration.
Now, the kinetic energy of an object can be written as:
K = (1/2)*m*v^2
where v is the velocity.
Now, when we drop the object, the potential energy begins to transform into kinetic energy, and by the conservation of the energy, by the moment that H is equal to zero (So the potential energy is zero) all the initial potential energy must now be converted into kinetic energy.
Uinitial = Kfinal.
m*g*H = (1/2)*m*v^2
v^2 = 2*g*H
v = √(2*g*H)
So we expressed the final velocity (the velocity at which the object impacts the ground) in terms of the height, H.
Answer:
6 gallons
Explanation:
At 30 mph, the fuel mileage is 25 mpg.
After 5 hours, the distance traveled is:
30 mi/hr × 5 hr = 150 mi
The amount of gas used is:
150 mi × (1 gal / 25 mi) = 6 gal
Answer:
Explanation:
Part 0
All the spring moves is 2 cm
x = 2 cm * [1 m / 100 cm ]
x = 0.020 meters
F = k*d
100N = k * 0.02 m
100 N / 0.02 = k
5000 N / m
Part A
The spring feels a force of 100 N - - 100N = 200 N because each person is pulling in the opposite direction.
F = k * x
200N = 5000 N/m * d
200 / 5000 = d
d = 0.04 meters.
Part B
10.2 kg must be converted to a force as experienced here on earth.
F = m * g
g = 9.81
m = 10.2
F = 10.2 * 9.81
F = 100.06 N
F = k * d
100.06 = 5000 * d
d = 100.06 / 5000
d = 0.02 meters.
Answer:
Explanation:
Given
mass 
Force 
door knob is located at a distance of r=0.8 m from axis
Angular acceleration of door 
Torque 
where I=moment of inertia


Answer:
(a): 
(b): 
(c): 
Explanation:
Given that an electron revolves around the hydrogen atom in a circular orbit of radius r = 0.053 nm = 0.053
m.
Part (a):
According to Coulomb's law, the magnitude of the electrostatic force of interaction between two charged particles of charges
and
respectively is given by

where,
= Coulomb's constant = 
= distance of separation between the charges.
For the given system,
The Hydrogen atom consists of a single proton, therefore, the charge on the Hydrogen atom, 
The charge on the electron, 
These two are separated by the distance, 
Thus, the magnitude of the electrostatic force of attraction between the electron and the proton is given by

Part (b):
The gravitational force of attraction between two objects of masses
and
respectively is given by

where,
= Universal Gravitational constant = 
= distance of separation between the masses.
For the given system,
The mass of proton, 
The mass of the electron, 
Distance between the two, 
Thus, the magnitude of the gravitational force of attraction between the electron and the proton is given by

The ratio
:
