A dog team driven by an Inuit hunter pulls two toboggans (Figure 1.49).
The dog team can apply a maximum force of 700 N. Each toboggan
experiences a constant frictional force of 100 N.
a) Determine the acceleration of the two toboggans, if each has a
mass of 300 kg.
b) What is the force in the rope joining the two toboggans together?
I know how to calculate the acceleration if there's no friction. Fnet=ma. 700N/600kg=a, but how do you do it if there's frictional force?
To calculate the acceleration of the two toboggans with the presence of frictional force, we will consider the net force acting on each toboggan individually.
a) To determine the acceleration of each toboggan, we will use the formula:
Net force = Mass × Acceleration
For the first toboggan:
Net force = Force applied by the dog team - Frictional force
Net force = 700 N - 100 N = 600 N
Using the formula:
600 N = Mass × Acceleration
Substituting the values:
600 N = 300 kg × Acceleration
or
Acceleration = 600 N / 300 kg
Simplifying:
Acceleration = 2 m/s²
Therefore, the acceleration of each toboggan is 2 m/s².
b) The force in the rope joining the two toboggans together is the force required to overcome the friction between the two toboggans. Since the force of friction is the same on both toboggans and acts in the opposite direction of their motion, the force in the rope will be equal in magnitude but opposite in direction.
Thus, the force in the rope will be:
Force in the rope = Frictional force = 100 N
Therefore, the force in the rope joining the two toboggans together is 100 N.
To calculate the acceleration of the two toboggans considering the frictional force, you need to modify the net force equation to include the frictional force.
a) The net force acting on an object is given by the difference between the applied force and the frictional force. So the modified equation becomes:
Fnet = Fapplied - Ffriction
In this case, the applied force is the maximum force the dog team can exert, which is 700 N. The frictional force on each toboggan is 100 N. Since there are two toboggans, the total frictional force is 2 * 100 N = 200 N.
Fnet = 700 N - 200 N = 500 N
Now, you can use the net force equation to calculate the acceleration:
Fnet = ma
500 N = (2 * m) * a
Since each toboggan has a mass of 300 kg, the total mass is 2 * 300 kg = 600 kg.
500 N = 600 kg * a
Dividing both sides of the equation by 600 kg:
a = 500 N / 600 kg
Calculating this, you will find the acceleration of the two toboggans.
b) To calculate the force in the rope joining the two toboggans together, you can use the same net force equation:
Fnet = Fapplied - Ffriction
In this case, the applied force is the maximum force the dog team can exert, which is 700 N. The frictional force on each toboggan is 100 N, so the total frictional force is 200 N.
Fnet = 700 N - 200 N = 500 N
Since the rope is connecting the two toboggans, the net force acting on one toboggan is also acting on the other toboggan in the opposite direction. Therefore, the force in the rope is equal to the net force:
Force in the rope = Fnet = 500 N
Hence, the force in the rope joining the two toboggans together is 500 N.