Answer:
The correct answer should be
A. 20 Joules
Explanation:
I'm taking the K12 Unit Test: Energy - Part 1 right now
The acceleration of the crate after it begins to move is 0.5 m/s²
We'll begin by calculating the the frictional force
Mass (m) = 50 Kg
Coefficient of kinetic friction (μ) = 0.15
Acceleration due to gravity (g) = 10 m/s²
Normal reaction (N) = mg = 50 × 10 = 500 N
<h3>Frictional force (Fբ) =?</h3>
Fբ = μN
Fբ = 0.15 × 500
<h3>Fբ = 75 N</h3>
- Next, we shall determine the net force acting on the crate
Frictional force (Fբ) = 75 N
Force (F) = 100 N
<h3>Net force (Fₙ) =?</h3>
Fₙ = F – Fբ
Fₙ = 100 – 75
<h3>Fₙ = 25 N</h3>
- Finally, we shall determine the acceleration of the crate
Mass (m) = 50 Kg
Net force (Fₙ) = 25 N
<h3>Acceleration (a) =?</h3>
a = Fₙ / m
a = 25 / 50
<h3>a = 0.5 m/s²</h3>
Therefore, the acceleration of the crate is 0.5 m/s²
Learn more on friction: brainly.com/question/364384
Answer:
Approximately 
, assuming friction between the vehicle and the ground is negligible.
Explanation:
Let 
denote the mass of the vehicle. Let 
denote the initial velocity of the vehicle. Let 
denote the spring constant (needs to be found.) Let 
denote the maximum displacement of the spring.
Convert velocity of the vehicle to standard units (meters per second):
.
Initial kinetic energy (
) of the vehicle:
.
When the vehicle is brought to a rest, the elastic potential energy (
) stored in the spring would be:
.
By the conservation of energy, if the friction between the vehicle and the ground is negligible, the initial 
of the vehicle should be equal to the 
of the vehicle. In other words:
.
Rearrange this equation to find an expression for , the spring constant:
.
Substitute in the given values 
, 
, and 
:
The speed of the space craft relative to the earth is given as: 0.024c. This is solved using the the equation for time dilation.
<h3>
What is time dilation?</h3>
Time dilation is the "slowing down" of a clock as determined by an observer in relative motion with regard to that clock under the theory of special relativity.
The formula is given as :
Δt = [Δr]/ √ 1 - (v²/c²)
Thus,
v = c√1 - (Δr/Δt)²
= c √(1 - (3600/3601)²
v = 0.024c
Learn more about time dilation at:
brainly.com/question/1933572
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