Three girls pull a sled. Determine the acceleration.

[Natko]

Homework Statement

Two girls pull a sled across a field of snow, as shown in the diagram. A third girl pulls backward with a 2.0 N force. If the mass of the sled is 10 kg, determine its instantaneous acceleration.

Homework Equations

F=ma

The Attempt at a Solution

Sorry, I'm stumped.

 

[BOYLANATOR]

You want to find the net force on the block. Do you have any ideas about how to work this out?

 

[MortalWombat]

To give some further input:

1) forces (pulling) are vectorial, which means they can be added by "putting them tip on tail". So, the net force is the sum over all forces.
2) Can you somehow determine the horizontal and vertical component of the forces?

 

[Natko]

You want to find the net force on the block. Do you have any ideas about how to work this out?

To give some further input:

1) forces (pulling) are vectorial, which means they can be added by "putting them tip on tail". So, the net force is the sum over all forces.
2) Can you somehow determine the horizontal and vertical component of the forces?

Thanks for the tips. I'll try:

F_y=10sin30-10sin40
=-1.428 N
F_x= 10cos30+10cos40-2
=14.32 N
√(F_y²+F_x²)=14.39 N
Θ=tan^-1(F_y/F_x)
=5.67
a=F/m
=1.439 m/s² [5.67 down of left]

Is that correct, or did I mess up somewhere? What does the question mean by "instantaneous?" I know what the word means, but how does it affect this question?

 

[BOYLANATOR]

Thanks for the tips. I'll try:

F_y=10sin30-10sin40
=-4.28 N

Numerical error in here. The rest of the working looks good

 

[BOYLANATOR]

Instantaneous means happening at this instant. It is unlikely that the girls could all pull with constant force in a constant direction for an extended time.