Respuesta :
(a) The total mass of the dogs is:
[tex]m_d = 8 \cdot (19.0 kg)=152.0 kg[/tex]
The mass of the sled is:
[tex]m_s=210 kg[/tex]
So, the total mass is: [tex]M=m_d+m_s=152 kg+210 kg=362 kg[/tex]
The total force exerted by the dogs is:
[tex]F=8 \cdot (185 N)=1480 N[/tex]
So, we can find the acceleration of the dogs by using Newton's second law:
[tex]a=\frac{F}{m}=\frac{1480 N}{362 kg}=4.09 m/s^2[/tex]
(b) The acceleration we found at point (a) is also the acceleration of the sled, which has a mass of 210 kg. Therefore, the force exerted by the dogs on the sled is equal to the product between the mass of the sled and its acceleration:
[tex]F=m_s a=(210 kg)(4.09 m/s^2)=859 N[/tex]
- The acceleration of the dogs as they pull the sled on the snow is [tex]\boxed{4.09\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}}[/tex] .
- The force experienced by the sled due to the dogs is [tex]\boxed{859\,{\text{N}}}[/tex] .
Further Explanation:
As the dogs collectively full the sled on the wet snow surface, the sled will experience a net force due to all the dogs acting on it.
Part (a):
The net force applied by the 8 dogs on the sled is:
[tex]\begin{aligned}{F_{{\text{net}}}}&=8\timesF\\&=8\times185\\&=1480\,{\text{N}}\\\end{aligned}[/tex]
The net mass of the dog and the sled combined is:
[tex]\begin{aligned}M&=\left({8\times{m_d}}\right)+{m_s}\\&=\left({8\times19}\right)+210\\&=362\,{\text{kg}}\\\end{aligned}[/tex]
The net acceleration of the dogs and the sled combined is:
[tex]a=\frac{{{F_{net}}}}{M}[/tex]
Substitute the values of net force and mass in above expression.
[tex]\begin{aligned}a&=\frac{{1480}}{{362}}\\&=4.088\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}\\&\approx4.09\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}\\\end{aligned}[/tex]
Thus, the acceleration of the dogs as they pull the sled on the snow is [tex]\boxed{4.09\,{{\text{m}}\mathord{\left/{\vphantom {{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}}[/tex] .
Part (b):
Since the sled is moving with an acceleration of [tex]4.09\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}[/tex] , the net force experienced by the sled due to the pull of the dogs is:
[tex]{F_{sled}}={m_s}\times a[/tex]
Substitute the values in above expression:
[tex]\begin{aligned}{F_{sled}}&=210\times4.09\\&=858.9\,{\text{N}}\\&\approx{\text{859}}\,{\text{N}}\\\end{aligned}[/tex]
Thus, the force experienced by the sled due to the dogs is [tex]\boxed{859\,{\text{N}}}[/tex] .
Learn More:
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Newton’s law of Motion
Keywords:
Team of eight dogs, waxed wood runners, loaded sled, with its rider, acceleration, average force 185 N, coupling between dog and sled, average masses of 19 kg each.
