Two objects are moving at equal speed along a level, frictionless surface. the second object has twice the mass of the first object. they both slide up the same frictionless incline plane. which object rises to a greater height?

When an object is sliding up in friction less surface than according to conservation of energy its potential energy will be converted into kinetic energy.

[tex]mgH=\frac{1}{2}mv^{2}\\ v=\sqrt{2gH}[/tex]

Here, m is the mass, v is the velocity, g is the acceleration due to gravity and H is the height.

Here the height is independent on the mass of an object and its only depend on velocity.

Now according to the question, two objects have same velocity but they have different masses.

Therefore, they rises to the same height because height will not change with mass.

johanrusli johanrusli · Answer 2 · 2020-01-04T04:05:45+01:00

Both objects rise to the same height

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Further explanation

Let's recall Kinetic Energy Formula as follows:

[tex]\large {\boxed{Ek = \frac{1}{2}mv^2} }[/tex]

Ek = Kinetic Energy ( Joule )

m = mass of the object ( kg )

v = speed of the object ( m/s )

Let us now tackle the problem !

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Given:

initial speed of first object = initial speed of second object = v

final speed of first object = final speed of second object = 0

mass of first object = m

mass of second object = 2m

Asked:

height = H = ?

Solution:

We will use Conservation of Energy to solve this problem:

[tex]Ep_1 + Ek_1 = Ep_2 + Ek_2[/tex]

[tex]0 + \frac{1}{2}mv^2 = mgH + 0[/tex]

[tex]\frac{1}{2}v^2 = gH[/tex]

[tex]v^2 = 2gH[/tex]

[tex]\boxed {H = \frac{v^2}{2g}}[/tex]

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[tex]H_1 : H_2 = \frac{v_1^2}{2g} : \frac{v_2^2}{2g}[/tex]

[tex]H_1 : H_2 = v_1^2 : v_2^2[/tex]

[tex]H_1 : H_2 = v^2 : v^2[/tex]

[tex]H_1 : H_2 = 1 : 1[/tex]

[tex]\boxed{ H_1 = H_2 }[/tex]

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Conclusion:

Both objects rise to the same height

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Learn more

Impacts of Gravity : https://brainly.com/question/5330244
Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454
The Acceleration Due To Gravity : https://brainly.com/question/4189441
Newton's Law of Motion: https://brainly.com/question/10431582
Example of Newton's Law: https://brainly.com/question/498822

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Answer details

Grade: High School

Subject: Physics

Chapter: Energy