An object having mass m is attached to a spring of force constant k oscillates with simple harmonic motion. The total mechanical
1 answer:
Answer:
The potential energy of the system is .
Explanation:
Given :
Mass of object , m .
Spring constant , k .
Total energy , E .
Maximum displacement , A .
We have to find potential energy when its kinetic energy is equal to 3/4E .
Now, we know :
Total energy is constant in simple harmonic motion.
Therefore ,
Total energy = Kinetic energy + potential energy .
Hence , this is the required solution.
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Answer:
a) Initial speed of the ball = 14.45 m/s
b) At height 6 m speed of ball = 9.55 m/s
c) Maximum height reached = 10.65 m
Explanation:
a) We have equation of motion , where s is the displacement, u is the initial velocity, t is the time taken and a is the acceleration.
s = 6 m, t = 0.5 seconds, a = acceleration due to gravity value = -9.8
Substituting
Initial speed of the ball = 14.45 m/s
b) We have equation of motion , where v is the final velocity
s = 6 m, u = 14.45 m/s, a = -9.8
Substituting
So at height 6 m speed of ball = 9.55 m/s
c) We have equation of motion , where v is the final velocity
u = 14.45 m/s, v =0 , a = -9.8
Substituting
Maximum height reached = 10.65 m
Given parameters:
Mass of the car = 1000kg
Unknown:
Height = ?
To find the heights for the different amount potential energy given, we need to understand what potential energy is.
Potential energy is the energy at rest due to the position of a body.
It is mathematically expressed as:
P.E = mgh
m is the mass
g is the acceleration due to gravity = 9.8m/s²
h is the height of the car
Now the unknown is h, height and we make it the subject of the expression to make for easy calculation.
h =
<u>For 2.0 x 10³ J;</u>
h = = 0.204m
<u>For 2.0 x 10⁵ J;</u>
h = = 20.4m
<u>For 1.0kJ = 1 x 10³J; </u>
h = = 0.102m