Interacting Systems - The Sled Dog

[mantillab]

Homework Statement

The sled dog in figure (attached) drags sleds A and B across the snow. The coefficient of friction between the sleds and the snow is 0.10.

If the tension in rope 1 is 150 N, what is the tension in rope 2?

Homework Equations

F_a on b = -F_b on a

The Attempt at a Solution

The force diagrams I did for sled A and sled B resulted in:

Sled A: Fnetx = T1 - (mu_k)(m_a)(g) = 52

Sled B: Fnetx = T2 -T1 - (mu_k)(m_b)(g) = T2 - 228.4

My solution for T2 = 280 is very close, but not the right solution. Should I be adding another force for sled B, based on the friction of sled A or another component of sled A?

 

[elyes]

can you help me please solving my problem thx

 

[mantillab]

Apparently the answer is 270N. Still don't know they determined that.

 

[Anadyne]

What are the masses of the sleds? I can't see the picture but I'm imagining that a dog is pulling sled b which is connected to sled a like so.

Dog--b--a

I don't know if this is what you meant, but Fnet for sled a and b are NOT the same unless they have the same mass.

 

[Kster]

Solution

T for rope 1:
100kg * a = 150 N
a = 1.5 m/s^2

If the tension in rope 1 is 150 N, what is the tension in rope 2?

T for rope 2:
(mass of sled 1 + sled 2)*1.5 m/s^2 = T
(100kg + 80kg)*1.5m/s^2 = 270N

 

[xstetsonx]

kster you ignored the friction force.
Rope 1:
T-Mkn=ma
150-0.10(100*9.8)=ma
rope 2 just the same expect for the weight is 180kg

 

[damionpitt]

So to Sum it all up...

Remember when dealing with any type of friction problem, you MUST add it into the eq. usually by finding the F_net along the y-axis.

F_net_y = m_1 *a_y (a_y = 0, since the object is not moving in the y-direction)

Find all forces acting on the y-axis to be your F_net_y

F_net_y = N - m*g
N - m *g = m_1 *a_y
N - m *g = 0
N = m *g

Also remember what your Friction Force is.

F_k = U_k * N
F_k = U_k * (m *g)

Now you can solve for a

T_1 - F_k = m_1 *a
(T_1 - F_k)/(m_1) = a
(T_1 - (U_k *(m_1 *g)))/(m_1) = a

Then you solve for T_2

T_2 - T_1 - F_k = m_2 * a
T_2 = (m_2 * a) + T_1 + F_k
T_2 = (m_2 * a) + T_1 + (U_k *( m_2 *g))