A 2.1 × 103 kg car starts from rest at the top of a driveway that is sloped at an angle of 20.0° with the horizontal. An average friction fo

Question

A 2.1 × 103 kg car starts from rest at the top of a driveway that is sloped at an angle of 20.0° with the horizontal. An average friction force of 4.0 × 103 N impedes the car’s motion so that the car’s speed at the bottom of the driveway is 3.8 m/s. What is the length of the driveway?

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Calantha 4 years 2021-07-26T15:57:26+00:00 1 Answers 1860 views 0

Answers ( )

  1. Ben
    3
    2021-07-26T15:59:09+00:00
    Reply

    Answer:

    The Length of the driveway is   4.98 m

    Explanation:

    we have to determine the length of the driveway  

    so we use following equations

    W=ΔK.E    where W is work and  ΔK.E   change in the kinetic energy

    also

    K.E = \frac{ MV^2}{2}

    also

    W = F.d  Where F is Force and d is distance

    Given that

    F_{f}= 4000 N   this frictional force

    m = 2100 Kg  

    θ= 20.0°  

    V=3.8 m/s   V is the car’s speed at the bottom of the driveway

    W=Δ K.E

    W = (1/2)(2100)(3.8)^2 =  15162  J  

    Since the x component of the gravity is

    Fx_ = mg sinФ

    so

    Fx_{} = (2100)(9.8)sin(20.0°  ) we get

    Fx_{} = 7038.77 N

    And the Net force is

    F_{net} = Fx_ {} – F_{f}

    F_{net} = 7038.77 – 4000 = 3038.77 N

    And the length of the driveway = W / (F_{net} ) = 15162/3038.77 = 4.98 m

    So this the length of the driveway.

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