(a) 1.08 J
The elastic potential energy stored in the block at any position x is given by

where
k is the spring constant
x is the displacement relative to the equilibrium position
Here we have
k = 860 N/m
x = 5.00 cm = 0.05 m is the position of the block
Substituting, we find

(b) 1.16 m/s
The total mechanical energy of the spring-mass system is equal to the potential energy found at point (a), because there the system was at its maximum displacement, where the kinetic energy (because the speed is zero).
At the equilibrium position, the mechanical energy is sum of kinetic and potential energy
E = K + U
However, at equilibrium position x = 0, so U = 0. Therefore, the kinetic energy is equal to the total energy found at point (a)

where
m = 1.60 kg is the mass of the block
v is the speed
Solving for v, we find

(c) 1.00 m/s
When the block is at position x = 2.50 cm, the mechanical energy is sum of kinetic and potential energy:

where
E = 1.08 J is the total mechanical energy
m = 1.60 kg is the mass
v is the speed
k = 860 N/m
x = 2.50 cm = 0.025 m is the displacement
Solving for v, we find

Answer:
v = 2.974
Explanation:
Perhaps the formula should be
v = √(2*g*d (sin(θ) - uk*cos(θ) ) This is a bit easier to read.
v = √(2* 9.80*0.725(0.707 - 0.12*0.707) ) Substitute values. Find 2*g*d
v = √14.21 * (0.707 - 0.0849) Figure out Sin(θ) - uk cos(θ)
v = √14.21 * (0.6222)
v = √8.8422 Take the square root of the value
v = 2.974
Electricity.
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In a home, the best option as a source of energy is electricity. Though some choose to use solar energy to power their devices, electricity is more cost effective.
Answer: 37.981 m/s
Explanation:
This situation is related to projectile motion or parabolic motion, in which the travel of the ball has two components: <u>x-component</u> and <u>y-component.</u> Being their main equations as follows:
<u>x-component:
</u>
(1)
Where:
is the point where the ball strikes ground horizontally
is the ball's initial speed
because we are told the ball is thrown horizontally
is the time since the ball is thrown until it hits the ground
<u>y-component:
</u>
(2)
Where:
is the initial height of the ball
is the final height of the ball (when it finally hits the ground)
is the acceleration due gravity
Knowing this, let's start by finding
from (2):
<u></u>
(3)
(4)
(5)
(6)
Then, we have to substitute (6) in (1):
(7)
And find
:
(8)
(9)
(10)
On the other hand, since we are dealing with constant acceleration (due gravity) we can use the following equation to find the value of the ball's final velocity
:
(11)
(12)
(13) This is the ball's final velocity, and the negative sign indicates its direction is downwards.
However, we were asked to find the <u>ball's final speed</u>, which is the module of the ball's final vleocity vector. This module is always positive, hence the speed of the ball just before it strikes the ground is 37.981 m/s (positive).
Answer:
Since your spine runs by your core, having a strong core will help protect and stabilize your spine, and you're also are able to control movements such as walking or standing better with a strong core.