A U.S. Department of Energy report estimates that over 100 billion kWh/year can be saved in the United States by various energy-
2 answers:
Answer:
(a). 12 plants
(b). 3171 $
Explanation:
(a)first convert units of 100 billion kWh/year into Watts(W)
also convert the units of 1000 MW into Watts(W)
1 billion = 10^9
1 year = 365*24 = 8760 hrs
so
100 billion kWh/year = 1
= W
1000 MW =
no. of plants = = 11.4
So 12 plants required
(b)
savings = unit price*total units
=
= 3170.9 =3171 $
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Answer:
44J
Explanation:
Given parameters:
Mass of rock = 0.22kg
Initial velocity = 20m/s
Distance moved = 10m
Unknown:
Initial kinetic energy of the rock = ?
Solution:
To solve this problem, we need to understand that kinetic energy is the energy due to the motion of a body.
It is mathematically expressed as;
Kinetic energy = m v²
m is the mass
v is the velocity
Kinetic energy = x 0.22 x 20² = 44J
Answer:
The sled required 9.96 s to travel down the slope.
Explanation:
Please, see the figure for a description of the problem. In red are the x and y-components of the gravity force (Fg). Since the y-component of Fg (Fgy) is of equal magnitude as Fn but in the opposite direction, both forces get canceled.
Then, the forces that cause the acceleration of the sled are the force of the wind (Fw), the friction force (Ff) and the x-component of the gravity force (Fgx).
The sum of all these forces make the sled move. Finding the resulting force will allow us to find the acceleration of the sled and, with it, we can find the time the sled travel.
The magnitude of the friction force is calculated as follows:
Ff = μ · Fn
where :
μ = coefficient of kinetic friction
Fn = normal force
The normal force has the same magnitude as the y-component of the gravity force:
Fgy = Fg · cos 30º = m · g · cos 30º
Where
m = mass
g = acceleration due to gravity
Then:
Fgy = m · g · cos 30º = 87.7 kg · 9.8 m/s² · cos 30º
Fgy = 744 N
Then, the magnitude of Fn is also 744 N and the friction force will be:
Ff = μ · Fn = 0.151 · 744 N = 112 N
The x-component of Fg, Fgx, is calculated as follows:
Fgx = Fg · sin 30º = m·g · sin 30º = 87.7 kg · 9.8 m/s² · sin 30º = 430 N
The resulting force, Fr, will be the sum of all these forces:
Fw + Fgx - Ff = Fr
(Notice that forces are vectors and the direction of the friction force is opposite to the other forces, then, it has to be of opposite sign).
Fr = 161 N + 430 N - 112 N = 479 N
With this resulting force, we can calculate the acceleration of the sled:
F = m·a
where:
F = force
m = mass of the object
a = acceleration
Then:
F/m = a
a = 479N/87.7 kg = 5.46 m/s²
The equation for the position of an accelerated object moving in a straight line is as follows:
x = x0 + v0 · t + 1/2 · a · t²
where:
x = position at time t
x0 = initial position
v0 = initial velocity
t = time
a = acceleration
Since the sled starts from rest and the origin of the reference system is located where the sled starts sliding, x0 and v0 = 0.
x = 1/2· a ·t²
Let´s find the time at which the position of the sled is 271 m:
271 m = 1/2 · 5.46 m/s² · t²
2 · 271 m / 5.46 m/s² = t²
<u>t = 9.96 s </u>
The sled required almost 10 s to travel down the slope.
Answer:
The newton’s second law is F=ma
The Gravitational force is
Explanation:
Given that,
The equivalent formulas for velocity, acceleration, and force using the relationships covered for UCM, Newton’s Laws, and Gravitation.
We know that,
Velocity :
The velocity is equal to the rate of position of the object.
....(I)
Acceleration :
The acceleration is equal to the rate of velocity of the object.
....(II)
Newton’s second Laws
The force is equal to the change in momentum.
In mathematically,
Put the value of p
Put the value from equation (II)
This is newton’s second laws.
Gravitational force :
The force is equal to the product of mass of objects and divided by square of distance.
In mathematically,
Where, m₁₂ = mass of first object
m= mass of second object
r = distance between both objects
Hence, The newton’s second law is F=ma
The Gravitational force is