Sam, whose mass is 72 kg , takes off across level snow on his jet-powered skis. The skis have a thrust of 190 N and a coefficient of kinetic

Question

Sam, whose mass is 72 kg , takes off across level snow on his jet-powered skis. The skis have a thrust of 190 N and a coefficient of kinetic friction on snow of 0.1. Unfortunately, the skis run out of fuel after only 9.0 s. How far has Sam traveled when he finally coasts to a stop?

in progress 0
Nem 1 year 2021-08-30T14:21:55+00:00 2 Answers 2 views 0

Answers ( )

    0
    2021-08-30T14:23:00+00:00

    Answer:

    181.11 m

    Explanation:

    Net Force is the sum of all the resultant force of all the forces acting on a body. The net force experienced by the jet is the difference of the Applied force and frictional force and this is represented in equation 1;

    [tex]F_{net} = F_{applied} – F_{friction} \\[/tex] ……………………….1

    but [tex]F_{friction}[/tex] = μmg …………………………………2

    Where μ is the coefficient of friction = 0.1

              m is the mass of the body = 72 kg

              g is the acceleration due to gravity 9.81 m/[tex]s^{2}[/tex]

    Substituting into equation 2 we have;

    [tex]F_{friction}[/tex] = 0.1 x 72 x 9.81

    [tex]F_{friction}[/tex] = 70.63 N

    Now we substitute our answer in equation 1;

    [tex]F_{net} = 190 N – 70.63 N \\[/tex]

    [tex]F_{net}[/tex] = 119.37 N

    We have to calculate the net acceleration in order to get our velocity .

    [tex]F_{net}[/tex] = m[tex]a_{net}[/tex]

    [tex]a_{net}[/tex] = [tex]\frac{F_{net}}{m}[/tex]

    [tex]a_{net}[/tex]  = [tex]\frac{119.37 N}{72 kg }[/tex]

    [tex]a_{net}[/tex]  = 1.66 [tex]m/s^{2}[/tex]

    Speed can be express as;

    v = u + at ……………….3

    where u is the initial velocity, which is 0 in this case.

    a is the net acceleration  = 1.66 [tex]m/s^{2}[/tex]

    t is the time which is 9 s

    substituting the values in equation 3 we have

    v =  1.66 [tex]m/s^{2}[/tex] x 9 s

    v = 14.94 m/s

    Calculating for Sam’s distance for the first 9 seconds, using the equation of motion we have;

    [tex]S_{1} = ut +\frac{1}{2}at^{2}[/tex]

    the jet was initially at rest so initial velocity is 0  and [tex]a_{net}[/tex]  = 1.66 [tex]m/s^{2}[/tex]

    [tex]S_{1} = \frac{1}{2} *1.66 m/s^{2} *9^{2}[/tex]

    [tex]S_{1}[/tex] = 67.23 m

    Also we have to calculate Sam’s distance after nine seconds using equations of motion express below;

    [tex]v^{2} -u^{2} = 2as[/tex]

    making S the subject formula we have;

    [tex]S_{2} =\frac{v^{2}-u^{2} }{2a}[/tex] ………………………………4

    v is the maximum velocity after the fuel finished  and its 14.94 m/s and a is the acceleration along the horizontal plane which put into consideration the coefficient of friction. a = μg = 0.1*9.8 m/[tex]s^{2}[/tex] = 0.98 m/[tex]s^{2}[/tex]

    We substitute our values into equation 4 to get our remaining distance;

    [tex]S_{2} = \frac{(14.94 m/s)^{2} }{2(0.98 m/s^{2} )}[/tex]

    [tex]S_{2}[/tex] = 113.88 m

    Therefore the total distance S = [tex]S_{1}[/tex] + [tex]S_{2}[/tex]

    S = 67.23 m + 113.88 m

    The total distance covered by Sam is 181.11 m

    0
    2021-08-30T14:23:22+00:00

    Given Information:

    Mass = 72 kg

    Force exerted by ski = 190 N

    coefficient of kinetic friction = 0.1

    ski runs out of fuel after = 9 sec

    Required Information:

    Distance traveled when he stops = ?

    Answer:

    d = 179.33 m

    Explanation:

    The problem can be divided into two parts

    Part 1: before running out of fuel

    In the first part, the forces acting on Sam are

    Ski thrust and Force of friction

    Force of friction = kmg

    where k is the coefficient of kinetic friction, m is Sam’s mass and g is gravity 9.8 m/s²

    Force of friction = 0.1*72*9.8

    Force of friction = 70.56 N

    so the net force acting on Sam is

    Fnet = ski thrust – force of friction

    Fnet = 190 – 70.56

    Fnet = 119.44 N

    According to Newton’s second law of motion

    F = ma

    a = F/m

    a = 119.44/72

    a = 1.65 m/s²

    The distance traveled can be found using kinematic equation

    d = vi + 0.5at²

    d = 0 + 0.5*1.65*9²

    d = 66.82 m

    The speed at this point is

    vf = (d + 0.5at²)/t

    vf = (66.82 + 0.5(1.65)(9)²)/9

    vf = 14.85 m/s

    Part 2: after running out of fuel

    When the fuel runs out the ski is no longer applying any force so the only force acting on Sam is force of friction

    kmg = ma

    kg = a

    a = 0.1*-9.8

    a = -0.98 (minus sign due to deceleration)

    The distance traveled can be found using kinematic equation

    2ad = vf² – vi²

    d = (vf² – vi²)/2a

    d = (vf² – vi²)/2a

    d = (0² – 14.85²)/2*-0.98

    d = 112.51 m

    How far has Sam traveled when he finally coasts to a stop?

    We have to sum the distance before and after Sam runs out of fuel because he stops after covering the sum of these distance

    d = 66.82 + 112.51

    d = 179.33 m

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )