Answer:
Explanation:
Using Hooke's law
Elastic potential energy = 1/2 K x²
K is elastic constant of the spring
x is the extension of the spring
a) The elastic potential energy when the spring is compressed twice as much Uel = 1/2 k (2x₀) ² = 4 (1/2 kx₀²)= 4 U₀
b) when is compressed half as much Uel = 1/2 k 
= 
( U₀)
c) make x₀ subject of the formula in the equation for elastic potential
x₀ =
x, the amount it will compressed to tore twice as much energy = 
x = √2 x₀
d) x₁, the new length it must be compressed to store half as much energy = 
x₁ = 
x₀
The acceleration should be a gain of 2 km/h per second
Answer: When your bike stops from brakes.
Explanation: Force and friction affect our daily lives in numerous amounts of ways. For instance, when a football is kicked, it moves faster later after some time its force decreases due to friction. A common example of friciton is when a bike stops. When the brakes are applied the friction on the pads cause the bike to stop.
Explanation:
The given data is as follows.
Mass, m = 75 g
Velocity, v = 600 m/s
As no external force is acting on the system in the horizontal line of motion. So, the equation will be as follows.
where, 
= mass of the projectile
= mass of block
v = velocity after the impact
Now, putting the given values into the above formula as follows.
![75(10^{-3}) \times 600 = [(75 \times 10^{-3}) + 50] \times v](https://tex.z-dn.net/?f=75%2810%5E%7B-3%7D%29%20%5Ctimes%20600%20%3D%20%5B%2875%20%5Ctimes%2010%5E%7B-3%7D%29%20%2B%2050%5D%20%5Ctimes%20v)
= 
v = 0.898 m/s
Now, equation for energy is as follows.
E = 
= 
= 13500 J
Now, energy after the impact will be as follows.
E' = ^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5B75%20%5Ctimes%2010%5E%7B-3%7D%20%2B%2050%5D%280.9%29%5E%7B2%7D)
= 20.19 J
Therefore, energy lost will be calculated as follows.
= E E'
= (13500 - 20) J
= 13480 J
And, n = 
= 
= 99.85
= 99.9%
Thus, we can conclude that percentage n of the original system energy E is 99.9%.
