A cart on a horizontal, linear track has a fan attached to it. The cart is positioned at one end of the track, and the fan is turned on. Starting from rest, the cart takes 4.22 s to travel a distance of 1.44 m. The mass of the cart plus fan is 350 g. Assume that the cart travels with constant acceleration.

Required:
a. What is the net force exerted on the cart-fan combination?
b. Mass is added to the cart until the total mass of the cart-fan combination is 656 g, and the experiment is repeated. How long does it take for the cart, starting from rest, to travel 1.63 m now?

Answer :

Answer:

a

  [tex]F = 0.0566 \ N[/tex]  

b

   [tex]t = 6.147 \ s[/tex]

Explanation:

From the question we are told that

     The distance travel in  4.22 s is  [tex]s = 1.44 \ m[/tex]

     The mass of the cart plus the fan is  [tex]m = 350 \ g = 0.35 \ kg[/tex]

Generally from kinematic equation we have that

        [tex]s = ut + \frac{1}{2} * a * t^2[/tex]

Here  u is the initial  velocity with value  [tex]u = 0 \ m/s[/tex]

So  

         [tex]1.44= 0 * t + \frac{1}{2} * a * 4.22^2[/tex]      

=>      [tex]a = 0.1617 \ m/s^2[/tex]

Generally the net force is  

         [tex]F = m * a[/tex]

=>      [tex]F = 0.35 * 0.1617[/tex]  

=>      [tex]F = 0.0566 \ N[/tex]  

Gnerally the new mass of the cart plus the fan is  [tex]M = 656 \ g = 0.656 \ kg[/tex]

    The distance considered is [tex]s_1 = 1.63 \ m[/tex]

     Generally the new acceleration of the cart is mathematically represented as

        [tex]F = M * a_1[/tex]

=>      [tex]a_1 = \frac{F}{M}[/tex]

=>      [tex]a_1 = \frac{0.0566}{0.656}[/tex]

=>      [tex]a_1 = 0.08628 \ m/s^2[/tex]

Gnerally from kinematic equation we have

          [tex]s = ut + \frac{1}{2} * a_1 * t ^2[/tex]

Here u  is the initial velocity and the value is zero because it started from rest  

=>       [tex]1.63 = 0 * t + \frac{1}{2} * 0.08628* t ^2[/tex]

=>        [tex]t = 6.147 \ s[/tex]

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