If the same pull instead acts over twice this distance,
C) The sled’s speed will be v√2 and its kinetic energy will be 2K.
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Further explanation
Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.
\(\large {\boxed {F = ma }\)
F = Force ( Newton )
m = Object's Mass ( kg )
a = Acceleration ( m )
Let us now tackle the problem !
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Complete Question:
A constant horizontal pull acts on a sled on a horizontal frictionless ice pond. The sled starts from rest. When the pull acts over a distance x, the sled acquires a speed v and a kinetic energy K. If the same pull instead acts over twice this distance:
A) The sled’s speed will be 2v and its kinetic energy will be 2K.
B) The sled’s speed will be 2v and its kinetic energy will be K√2.
C) The sled’s speed will be v√2 and its kinetic energy will be 2.
D) The sled's speed will be v√2 and its kinetic energy will be K√2.
E) The sled's speed will be 4v and its kinetic energy will be 2K.
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We will use following formula to solve this problem:
\(w = \Delta K\)
\(Fx = K - 0\)
\(\large {\boxed {K = Fx} }\)
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Let's compare the two situations by using above formula:
\(K_1 : K_2 = F_1x_1 : F_2x_2\)
\(K : K_2 = Fx : F(2x)\)
\(K : K_2 = 1 : 2\)
\(K_2 = 2K\)
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\(K_1 : K_2 = \frac{1}{2}m(v_1)^2: \frac{1}{2}m(v_2)^2\)
\(K : 2K = (v)^2: (v_2)^2\)
\(1 : 2 = (v)^2: (v_2)^2\)
\((v_2)^2 = 2v^2\)
\(v_2 = \sqrt{2v^2}\)
\(v_2 = v\sqrt{2}\)
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Conclusion:
If the same pull instead acts over twice this distance,
C) The sled’s speed will be v√2 and its kinetic energy will be 2K.
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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
