identify whether each of the following is a former of mechanical energy: elastic potential energy, chemical potential energy, gr
1 answer:
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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:
Answer:
a)
b)
c)
d) or 18.3 cm
Explanation:
For this case we have the following system with the forces on the figure attached.
We know that the spring compresses a total distance of x=0.10 m
Part a
The gravitational force is defined as mg so on this case the work donde by the gravity is:
Part b
For this case first we can convert the spring constant to N/m like this:
And the work donde by the spring on this case is given by:
Part c
We can assume that the initial velocity for the block is Vi and is at rest from the end of the movement. If we use balance of energy we got:
And if we solve for the initial velocity we got:
Part d
Let d1 represent the new maximum distance, in order to find it we know that :
And replacing we got:
And we can put the terms like this:
If we multiply all the equation by 2 we got:
Now we can replace the values and we got:
And solving the quadratic equation we got that the solution for or 18.3 cm because the negative solution not make sense.
