Respuesta :
Answer: (a) Acceleration of the dogs starting from rest if each dog exerts an average force of 185 N backward on the snow is 2.88 [tex]m/s^{2}[/tex].
(b) The force in the coupling between the dogs and the sled is 1041.74 N.
Explanation:
(a) Formula to calculate acceleration is as follows.
[tex]\sum F_{x} = 8F_{d} - f_{s(max)}[/tex]
= [tex](m_{s} + 8m_{d})a[/tex]
a = [tex]\frac{8F_{d} - \mu_{s}m_{s}g}{m_{s} + 8m_{d}}[/tex]
= [tex]\frac{8(185 N) - (0.14)(245)(9.8)}{245 + 8(19.0 kg)}[/tex]
= [tex]\frac{1480 - 336.14}{397}[/tex]
= [tex]\frac{1143.86}{397}[/tex]
= 2.88 [tex]m/s^{2}[/tex]
Therefore, acceleration of the dogs starting from rest if each dog exerts an average force of 185 N backward on the snow is 2.88 [tex]m/s^{2}[/tex].
(b) According to Newton's second law of motion we will calculate the value of T as follows.
[tex]\sum F_{x} = T - f_{s(max)} = m_{s}a[/tex]
T = [tex]m_{s}a + \mu_{s}m_{s}g[/tex]
= [tex]245(2.88 m/s^{2}) + (0.14)(245)(9.8)[/tex]
= 705.6 + 336.14
= 1041.74 N
Therefore, we can conclude that the force in the coupling between the dogs and the sled is 1041.74 N.
