Respuesta :
Answer:
kinetic energy of glider = -0.376 j
Explanation:
Original distance by which the spring is compressed can be determine by using law of conservation of energy (As spring slide from glider, it gain some potential energy. On the top of track there is glider’s potential energy exist)
[tex]\frac{1}{2} kx^2 = mgh[/tex]
where x is compressed distance by spring
height of track is calculated as
[tex] sin\theta \frac{h}{l}[/tex]
[tex]h = l sin\theta[/tex]
where l is distance covered by glider, theta angle is the angle of inclination of track
therefore, we have formula for x as
[tex]x = \sqrt{\frac{2mglsin\theta}{k}}[/tex]
[tex]x = \sqrt{\frac{2\times 0.05 \times 9.8 \times 1.50\times sin39}{600}}[/tex]
x = 0.039 m
kinetic energy of glider = potential energy by spring - potential energy at 1.50 distance
[tex]=( \frac{1}{2} \times 600\times 0.039^2) - (0.05 \times 9.8 \times 1.5 \times sin 39)[/tex]
kinetic energy of glider = -0.376 j
The kinetic energy of the glider at this point (x) is equal to -0.376 Joules.
Given the following data:
Angle of inclination = 39.0°.
Mass of glider = [tex]5.00 \times 10^{-2}\;kg[/tex].
Spring constant = 600 N/m.
Length = 1.50 m.
How to calculate the kinetic energy of the glider.
Since the glider obeys Hooke’s law and the length (distance) of the glider is known, we would apply the law of conservation of energy:
[tex]\frac{1}{2} kx^2=mgdsin \theta[/tex]
Where:
- k is the spring constant.
- m is the mass.
- g is acceleration due to gravity.
- x is the extension.
Making x the subject of formula, we have:
[tex]x=\sqrt{\frac{2mgdsin\theta}{k} } \\\\x=\sqrt{\frac{2 \times 5.00 \times 10^{-2}\times 9.8 \times sin39}{600} } \\\\[/tex]
x = 0.039 meter.
Now, we can calculate the kinetic energy of the glider at this point (x):
[tex]K.E = \frac{1}{2} kx^2-mgdsin\theta\\\\K.E = \frac{1}{2}\times 600 \times 0.039^2-5.00 \times 10^{-2}\times 9.8 \times sin39[/tex]
K.E = -0.376 Joules.
Read more on spring constant here: https://brainly.com/question/25313999
