The second projectile was about 1.7 times faster than the first.
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Further explanation
Let's recall Kinetic Energy Formula as follows:
\(Ek = \frac{1}{2}mv^2\)
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:
height of pendulum 1 = h₁ = 2.0 cm
height of pendulum 2 = h₂ = 5.5 cm
Asked:
speed of projectile 2 = v₂ = ?
Solution:
Firstly , we will use Conservation of Energy as follows:
\(Ek = Ep\)
\(\frac{1}{2}(m+M)v^2 = (m+M)gh\)
\(\frac{1}{2}v^2 = gh\)
\(v^2 = 2gh\)
\(v = \sqrt{2gh}\)
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Next, we will use Conservation of Momentum to find the speed of projectile:
\(mv' = ( m + M )v\)
\(v' = (1 + \frac{M}{m})v\)
\(v' = (1 + \frac{M}{m}) \sqrt{2gh}\)
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Finally , we will compare speed of projectiles of the two experiments as follows:
\(v_1' : v_2' = (1 + \frac{M}{m})\sqrt{2gh_1} : (1 + \frac{M}{m})\sqrt{2gh_2}\)
\(v_1' : v_2' = \sqrt{h_1} : \sqrt{h_2}\)
\(v_1' : v_2' = \sqrt{2.0} : \sqrt{5.5}\)
\(v_2' = \sqrt{\frac{5.5}{2.0}} \times v_1'\)
\(v_2' = 1.7 v_1'\)
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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: Dynamics
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Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant
