Answer:
v = 0.41 m/s
Explanation:
- In this case, the change in the mechanical energy, is equal to the work done by the fricition force on the block.
- At any point, the total mechanical energy is the sum of the kinetic energy plus the elastic potential energy.
- So, we can write the following general equation, taking the initial and final values of the energies:

- Since the block and spring start at rest, the change in the kinetic energy is just the final kinetic energy value, Kf.
- ⇒ Kf = 1/2*m*vf² (2)
- The change in the potential energy, can be written as follows:

where k = force constant = 815 N/m
xf = final displacement of the block = 0.01 m (taking as x=0 the position
for the spring at equilibrium)
x₀ = initial displacement of the block = 0.03 m
- Regarding the work done by the force of friction, it can be written as follows:

where μk = coefficient of kinettic friction, Fn = normal force, and Δx =
horizontal displacement.
- Since the surface is horizontal, and no acceleration is present in the vertical direction, the normal force must be equal and opposite to the force due to gravity, Fg:
- Fn = Fg= m*g (5)
- Replacing (5) in (4), and (3) and (4) in (1), and rearranging, we get:


- Replacing by the values of m, k, g, xf and x₀, in (7) and solving for v, we finally get:

1) At the moment of being at the top, the piston will not only tend to push the penny up but will also descend at a faster rate at which the penny can reach in 'free fall', in that short distance. Therefore, at the highest point, the penny will lose contact with the piston. Therefore the correct answer is C.
2) To solve this problem we will apply the equations related to the simple harmonic movement, hence we have that the acceleration can be defined as

Where,
a = Acceleration
A = Amplitude
= Angular velocity
From a reference system in which the downward acceleration is negative due to the force of gravity we will have to



From the definition of frequency and angular velocity we have to




Therefore the maximum frequency for which the penny just barely remains in place for the full cycle is 2.5Hz
Answer:
$4.2
Explanation:
Given data
Power= 700W
time= 10 hours
Cost per kilowatt hours is cents $0.20
Let us find the number of hours in a month
=24*30
=720 hours
Energ= power*time
Energy= 700/1000*30
Energy= 7*3
Enery= 21 kwh
1 kwh= 0.2
21kwh= x
cross multiply
x=21*0.2
x= $4.2
This is a binary star system
A light meter, because illu is a root for light