Question

A team of eight dogs pulls a sled with waxed wood runners on wet snow (mush!). The dogs have average masses of 19.0 kg, and the loaded sled with its rider has a mass of 210 kg. (a) Calculate the acceleration of the dogs starting from rest if each dog exerts an average force of 185 N backward on the snow. (b) Calculate the force in the coupling between the dogs and the sled.

Answer 1

• The acceleration of the dogs as they pull the sled on the snow is $\boxed{4.09\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}}$ .

• The force experienced by the sled due to the dogs is $\boxed{859\,{\text{N}}}$ .

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:

$\begin{aligned}{F_{{\text{net}}}}&=8\timesF\\&=8\times185\\&=1480\,{\text{N}}\\\end{aligned}$

The net mass of the dog and the sled combined is:

$\begin{aligned}M&=\left({8\times{m_d}}\right)+{m_s}\\&=\left({8\times19}\right)+210\\&=362\,{\text{kg}}\\\end{aligned}$

The net acceleration of the dogs and the sled combined is:

$a=\frac{{{F_{net}}}}{M}$

Substitute the values of net force and mass in above expression.

$\begin{aligned}a&=\frac{{1480}}{{362}}\\&=4.088\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}\\&\approx4.09\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}\\\end{aligned}$

Thus, the acceleration of the dogs as they pull the sled on the snow is $\boxed{4.09\,{{\text{m}}\mathord{\left/{\vphantom {{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}}$ .

Part (b):

Since the sled is moving with an acceleration of $4.09\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}$ , the net force experienced by the sled due to the pull of the dogs is:

${F_{sled}}={m_s}\times a$

Substitute the values in above expression:

$\begin{aligned}{F_{sled}}&=210\times4.09\\&=858.9\,{\text{N}}\\&\approx{\text{859}}\,{\text{N}}\\\end{aligned}$

Thus, the force experienced by the sled due to the dogs is $\boxed{859\,{\text{N}}}$ .

Learn More:

1. A 30.0-kg box is being pulled across a carpeted floor by a horizontal force of 230 N brainly.com/question/7031524

2. A horizontal rope is tied to a 50 kg box brainly.com/question/2416204

3. Why is it important to define a frame of reference brainly.com/question/526888

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.

Answer 2

(a) The total mass of the dogs is:

$m_d = 8 \cdot (19.0 kg)=152.0 kg$

The mass of the sled is:

$m_s=210 kg$

So, the total mass is: $M=m_d+m_s=152 kg+210 kg=362 kg$

The total force exerted by the dogs is:

$F=8 \cdot (185 N)=1480 N$

So, we can find the acceleration of the dogs by using Newton's second law:

$a=\frac{F}{m}=\frac{1480 N}{362 kg}=4.09 m/s^2$

(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:

$F=m_s a=(210 kg)(4.09 m/s^2)=859 N$