Physics
maggalil000
37

Suppose that a sled is accelerating at a rate of 2 m/s2. If the net force is tripled and the mass is halved, then what is the new acceleration of the sled? (show how you solved it)

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(1) Answers
karla519

Start with Newton's 2nd law of motion:                              Force = (mass) x (acceleration) . Since we're going to be talking about acceleration, lets divide each side by (mass):                              Acceleration = (force) / (mass) . OK.  We start out with a certain acceleration 'A₀'.  It's the result of a certain force 'F₀' and a certain mass 'M₀'.  (I used the little subscripts " ₀ " to show that these are the originals, before any changes.)              Original acceleration = (Original force) / (original mass)                               A₀             =          F₀            /        M₀ . Now you want to triple the force and cut the mass in half:                       New acceleration  A₁ = (3 F₀) / (1/2 M₀) . Divide each side by 3:           A₁ / 3  =  F₀ / (1/2 M₀) . Multiply each side by  1/2 :   (1/2 A₁) / 3  =  F₀/M₀                                                    A₁ / 6  =  F₀/M₀ Take a look at the right side of that equation . . .  F₀/M₀ . That's just the original acceleration  A₀ . So now, after the change, we have                 A₁ / 6  =  A₀ . You asked "What is the new acceleration ?" OK.  Multiply each side by  6  :                        A₁ = 6 A₀ . Whatever the original acceleration was, the new acceleration is 6 times as much. If it was originally  2 m/s², then after the change, it becomes  (6 x 2)  =  12 m/s² .

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