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:

Answer 1

W₁ = F * x = 1/2 * m * v₁²

W₂ = F * 2x = 2 * 1/2 * m * v₂² = 1/2 * m * (√2 * v₂)²

v₁ = √2 * v₂

Answer 2

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

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics