Answer:
B) The car at point C has less kinetic energy than the car at point B.
Explanation:
We have two types of energy involved in this situation:
- Gravitational potential energy: this is the energy related to the heigth of the car, and it is given by 
, where m is the mass of the car, g is the gravitational acceleration, and h is the heigth of the car. The potential energy is higher when the car is located higher above the ground.
- Kinetic energy: this is the energy due to the motion of the car, and it is given by 
, where m is the mass of the car and v is its speed. The kinetic energy is higher when the speed of the car is higher.
- The law of conservation of energy states that the total mechanical energy of the car (sum of potential energy and kinetic energy: 
) is constant). This implies that when the car is at a higher point, the kinetic energy is less (because U is larger, so K must be smaller), while when the car is at a lower point, the kinetic energy is larger.
- Based on what we have written so far, we can conclude that the correct statement is:
B) The car at point C has less kinetic energy than the car at point B.
Because the car at point C is located at a higher point than point B, so the car at point C has larger potential energy than at point B, which implies that car at point C has less kinetic energy than the car at point B.
<span>Orbital radius would decrease because the gravitational pull would increase.</span>
Answer:
0.19
Explanation:
mass of block, m = 40 kg
F = 150 N
Angle make with the horizontal, θ = 60 degree
Let μ be the coefficient of kinetic friction
The component of force along horizontal direction is F Cos θ
= 150 cos 60 = 75 N
As it is moving with constant velocity it mean the acceleration of the block is zero.
Applied force in horizontal direction = friction force
75 = μ x Normal reaction
75 = μ x m x g
75 = μ x 40 x 9.8
μ = 0.19
Thus, the coefficient of kinetic friction is 0.19.
I assume you meant to say
Given that <em>x</em> = √3 and <em>x</em> = -√3 are roots of <em>f(x)</em>, this means that both <em>x</em> - √3 and <em>x</em> + √3, and hence their product <em>x</em> ² - 3, divides <em>f(x)</em> exactly and leaves no remainder.
Carry out the division:
To compute the quotient:
* 2<em>x</em> ⁴ = 2<em>x</em> ² • <em>x</em> ², and 2<em>x</em> ² (<em>x</em> ² - 3) = 2<em>x</em> ⁴ - 6<em>x</em> ²
Subtract this from the numerator to get a first remainder of
(2<em>x</em> ⁴ + 3<em>x</em> ³ - 5<em>x</em> ² - 9<em>x</em> - 3) - (2<em>x</em> ⁴ - 6<em>x</em> ²) = 3<em>x</em> ³ + <em>x</em> ² - 9<em>x</em> - 3
* 3<em>x</em> ³ = 3<em>x</em> • <em>x</em> ², and 3<em>x</em> (<em>x</em> ² - 3) = 3<em>x</em> ³ - 9<em>x</em>
Subtract this from the remainder to get a new remainder of
(3<em>x</em> ³ + <em>x</em> ² - 9<em>x</em> - 3) - (3<em>x</em> ³ - 9<em>x</em>) = <em>x</em> ² - 3
This last remainder is exactly divisible by <em>x</em> ² - 3, so we're left with 1. Putting everything together gives us the quotient,
2<em>x </em>² + 3<em>x</em> + 1
Factoring this result is easy:
2<em>x</em> ² + 3<em>x</em> + 1 = (2<em>x</em> + 1) (<em>x</em> + 1)
which has roots at <em>x</em> = -1/2 and <em>x</em> = -1, and these re the remaining zeroes of <em>f(x)</em>.
