If a spring with a spring constant k = 10 N/m
is stretched from its equilibrium position by
0.1 m, and released, what would be the maxi-
mum kinetic energy at any time in its motion?
Neglect friction.
1. 0.025 J
2. 0.1 J
3. Not enough information given
4. 0.05 J
5. 1 J
wouldn't KEmzx= 1/2k(.1)^2=.05joules?
the answer is 4. 0.05 J
To find the maximum kinetic energy of the spring, we can use the principle of conservation of mechanical energy.
The potential energy stored in the spring when it is stretched by 0.1 m can be calculated using the formula:
Potential Energy (PE) = (1/2) k x^2
where k is the spring constant and x is the displacement from the equilibrium position.
Plugging in the given values, we have:
PE = (1/2) * 10 N/m * (0.1 m)^2
= 0.5 N * m
Since there is no friction and neglecting any other losses of energy, all of the potential energy will be converted into kinetic energy when the spring is released.
Therefore, the maximum kinetic energy of the spring is 0.5 N * m.
However, in the provided answer options, none of the choices match this value. Thus, the correct answer is option 3: Not enough information given.
To find the maximum kinetic energy of the spring, we need to calculate the maximum displacement of the spring and use the formula for potential energy of a spring.
The potential energy stored in a spring is given by the formula:
PE = (1/2) kx^2
Where:
PE is the potential energy stored in the spring
k is the spring constant
x is the displacement from the equilibrium position
In this case, we are given the spring constant k = 10 N/m and the displacement x = 0.1 m.
Now, the maximum displacement of the spring will occur when all the potential energy is converted into kinetic energy. At this point, the kinetic energy is at its maximum.
The total mechanical energy of the system remains constant, so we can equate the potential energy to the kinetic energy:
PE = KE
Therefore, the maximum kinetic energy is given by:
KE = (1/2) kx^2
Substituting the given values, we get:
KE = (1/2) * 10 N/m * (0.1 m)^2
= (1/2) * 10 N/m * 0.01 m^2
= (1/2) * 10 * 0.01
= 0.05 J
Therefore, the maximum kinetic energy at any time in its motion is 0.05 J.
So, the correct option is 4. 0.05 J.