The drawing shows an object attached to an ideal spring, which is hanging from the ceiling. The unstrained length of the spring
is indicated. For purposes of measuring the height h that determines the gravitational potential energy, the floor is taken as the position where h = 0 m. The equilibrium position at which the object hangs stationary is identified as position 2. The object is set into vertical simple harmonic motion between positions 1 and 3. Identify the positions where the kinetic energy KE, the elastic potential energy EPE, and the gravitational potential energy GPE each have their maximum values during an oscillation cycle.
1 answer:
Image is missing so I have attached it.
Also, the options are missing and it is;
A) KE is has a maximum value at position 3. EPE has a maximum value at position 2. GPE has a maximum value at position 1.
B) KE is has a maximum value at position 1. EPE has a maximum value at position 2. GPE has a maximum value at position 3.
C) KE is has a maximum value at position 2. EPE has a maximum value at position 3. GPE has a maximum value at position 1.
D) KE is has a maximum value at position 1. EPE has a maximum value at position 3. GPE has a maximum value at position 2.
E) KE is has a maximum value at position 2. EPE has a maximum value at position 1. GPE has a maximum value at position 3.
Answer:
Option C is the correct answer which says; KE is has a maximum value at position 2. EPE has a maximum value at position 3. GPE has a maximum value at position 1.
Explanation:
If an object vibrates about its mean position, under the influence of a restoring force, such that restoring force is directly proportional to the displacement from the mean position, the motion of the object is called simple harmonic motion. During Simple harmonic motion, the sum of Kinetic and potential energy remains constant.
Now, Looking at the diagram, Kinetic Energy (KE) is maximum at position 2.
Looking at the options, only C and E agree with this.
Thus, our answer is either option C or E.
However, Option E is not going to be right because it says that GPE is at a maximum at position 3, which is not true as the maximum GPE will occur at position 1.
Thus,
Option C fulfills that and therefore will be the correct answer.
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Answer:
v_average = 15 m / s
Explanation:
The average speed can be found in two ways,
* taking the distance traveled and divide it by the time spent
* taking the velocities in each time interval and then finding the weighted average by the time fraction
v_average = 1 / t_total ∑ vi ti
Let's apply this last equation
Total time is
t = t₁ + t₂
t = 10 + 10 = 20 min
v_average = 10/20 10 + 10/20 20
v_average = 10/2 + 20/2
v_average = 15 m / s
The expression commonly used for potential gravitational energy is just simplification. It is actually just the first term in Taylor expansion of the real expression.
In general, the potential energy of gravitational field is defined as:
Where G is universal gravitational constant, and r is the distance between the objects centers of mass. Negative sign represents the bound state.
Since we are not given the mass of the planet we have to calculate it.
This formula can be used for any planet. It gives you the gravitational acceleration on the planet's surface. We can use it to calculate the planet's mass:
Now we can calculate the potential energy of that cannonball when it reaches its maximum height.
When we plug in the numbers we get:
The potential energy has to be equal to the kinetic energy.
In general, the potential energy of gravitational field is defined as:
Where G is universal gravitational constant, and r is the distance between the objects centers of mass. Negative sign represents the bound state.
Since we are not given the mass of the planet we have to calculate it.
This formula can be used for any planet. It gives you the gravitational acceleration on the planet's surface. We can use it to calculate the planet's mass:
Now we can calculate the potential energy of that cannonball when it reaches its maximum height.
When we plug in the numbers we get:
The potential energy has to be equal to the kinetic energy.