Determine the acceleration of the sled

[wick85]

Homework Statement

A 4.41 kg penguin sits on a 11.5 kg sled, as seen in the figure below.


A horizontal force of F = 58.7 N is applied to the sled, but the penguin attempts to impede the motion by holding onto a cord attached to a tree. The coefficient of kinetic friction between the sled and snow as well as that between the sled and the penguin is 0.150.

Determine the tension in the cord.

Determine the acceleration of the sled.

Homework Equations

a=F/m

T=UkN/cos theta

The Attempt at a Solution

I'm having problems setting this up, so I haven't been able to make a decent attempt at it.

The attached picture is the penguin.

 

[rl.bhat]

Find the frictional force fs between sled and the snow. It acts towards the tree. An equal and opposite reactionary force acts on the penguin.
Find the frictional force fp between penguin and sled. It acts away from the tree. Find total force acting on penguin. From that you can find the tension in the cord.

 

[tomcue]

I would approach this problem by first identifying the known and unknown variables. The known variables are the masses of the penguin and sled, the applied force, and the coefficients of kinetic friction. The unknown variables are the tension in the cord and the acceleration of the sled.

To determine the tension in the cord, I would use the equation T=UkN/cos θ, where Uk is the coefficient of kinetic friction, N is the normal force, and θ is the angle between the cord and the horizontal plane. Since the penguin is attempting to impede the motion, the angle θ would be 180 degrees. The normal force, N, can be calculated by multiplying the mass of the penguin by the acceleration due to gravity, 9.8 m/s^2.

Next, I would use the equation a=F/m to determine the acceleration of the sled. The force, F, in this case, would be the applied force of 58.7 N minus the tension in the cord. The mass, m, would be the combined mass of the penguin and sled.

Finally, I would plug in the known values and solve for the unknown variables. The tension in the cord can be found using the equation T=0.15(4.41 kg + 11.5 kg)(9.8 m/s^2)/cos 180 degrees, which gives a tension of approximately 145 N.

To determine the acceleration of the sled, I would use the equation a=(58.7 N - 145 N)/(4.41 kg + 11.5 kg), which gives an acceleration of approximately -5.01 m/s^2. The negative sign indicates that the sled is decelerating.

In conclusion, the tension in the cord is 145 N and the acceleration of the sled is -5.01 m/s^2. This means that the penguin is successfully impeding the motion of the sled, causing it to slow down.