2. Two toy cars are involved in a race. Car A has mass m while car B has mass 2m. a. The two cars have the same force applied to them over a

Question

2. Two toy cars are involved in a race. Car A has mass m while car B has mass 2m. a. The two cars have the same force applied to them over a distance of 1 meter. Which car has a larger kinetic energy after traveling 1 meter? Which car has a larger momentum after traveling 1 meter? Explain your answers. b. The two cars have the same force applied to them over a time period of 10 seconds. Which car has a larger kinetic energy after 10 seconds? Which car has a larger momentum after 10 seconds? Explain your answers.

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Thành Đạt 7 months 2021-07-20T05:28:35+00:00 1 Answers 12 views 0

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    2021-07-20T05:30:27+00:00

    Answer:

    a) The kinetic energy of the two cars is the same

    the moment of car 2 is greater than the moment of car 1

    b)  the kinetic energy of car 1 is greater than that of car 2

    the moment of the two cars is the same

    Explanation:

    a) to know the kinetic energy of each car, we must find the speed, use Newton’s second law to find the acceleration

    Car 1

         F = m a

        a = F / m

    Let’s use kinematics to find the velocity after x = 1 m

           v² = v₀² + 2 a x

    The initial speed is zero

           v = √ (2 F/m  x)

    For the distance of x = 1 m

            v₁ = √ (2 F / m)

    Car 2

          F = 2m a

          a = F / 2m

          v² = 2 a x

          v = √ (F/m  x)

     For x = 1 m

           v₂ = √(F / m)

    Let’s calculate the kinetic energy of each car

    Car 1

          K₁ = ½ m v₁²

          K₁ = ½ m 2F / m

          K₁ = F

    Car 2

          K₂ = ½ 2m v₂²

          K₂ = ½ 2m F / m

          K₂ = F

    The kinetic energy of the two cars is the same

    Let’s calculate the moment

    Car 1

       P₁ = m v₁

       P₁ = m √ (2F / m)

    Car 2

        P₂ = 2m v²

        P₂ = 2m √(F / m)

    We see that the moment of car 2 is greater than the moment of car 1

    b) in this part the force is applied by t = 10 s

    Acceleration is the same, let’s find the speed

    Car1

              v = v₀ + a t

              v = F / m t

              v₁ = F / m 10

    Car 2

               v₂ = F / 2m 10

               v₂ = F / m 5

    Let’s calculate the kinetic energy of each car

    Car 1

               K₁ = ½ m v₁²

               K₁ = ½ m (F / m 10)²

               K₁ = 50 F² / m

    Car2

             K₂ = ½ 2m v₂²

             K₂ = m (F / m 5)²

             K₂ = 25 F² / m

    In this case we see that the kinetic energy of car 1 is greater than that of car 2

    Let’s calculate the moment

    Car 1

             P₁ = m v₁

             P₁ = m F / m 10

             P₁ = 10 F

     

    Car 2

            P₂ = 2m v₂

            P₂ = 2m F / m 5

            P₂ = 10 F

    In this case the moment of the two cars is the same

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