A 5.0 kg penguin sits on top of a 12 kg sled, as in the figure. A horizontal force of 45 N is applied to the sled, but the penguin keeps himself stationary by holding onto a string attached to the wall. The coefficient of kinetic friction between the penguin and the sled is 0.18, and the coefficient of kinetic friction between the sled and the snow is 0.14.

To solve this problem, we need to consider the forces acting on the system and apply Newton's laws of motion. Let's break it down step by step:

Step 1: Identify the forces acting on the system.
- The tension force in the string: Tension (T).
- The force applied to the sled: Applied force (Fapplied).
- The force of kinetic friction between the penguin and the sled: Friction force between penguin and sled (Fps).
- The force of kinetic friction between the sled and the snow: Friction force between sled and snow (Fsnow).

Step 2: Determine the direction of each force.
- Tension force in the string acts in the horizontal direction opposite to the applied force.
- Applied force acts in the horizontal direction towards the right.
- The friction forces (Fps and Fsnow) act in the opposite direction to the motion.

Step 3: Calculate the friction forces.
- The friction force between the penguin and the sled is given by:
Fps = μps * normal force between the penguin and the sled.

- The friction force between the sled and the snow is given by:
Fsnow = μsnow * normal force between the sled and the snow.

Step 4: Find the normal forces.
- The normal force between the penguin and the sled is equal to the weight of the penguin:
Normal force between the penguin and the sled = m_penguin * g, where g is the acceleration due to gravity.

- The normal force between the sled and the snow is equal to the weight of the sled:
Normal force between the sled and the snow = m_sled * g.

Step 5: Calculate the friction forces using the obtained normal forces and coefficients of friction.

Step 6: Apply Newton's second law.
- The sum of the forces in the horizontal direction is equal to the mass of the system multiplied by acceleration (F_net = m_total * a).
- The net force acting on the system is the difference between the applied force and the friction forces (F_net = F_applied - F_ps - F_snow).

Step 7: Solve for acceleration.
- Set up the equation from step 6 and solve for the acceleration.

Now, let's apply these steps to the given problem.

Step 1: Identify the forces acting on the system.
- Tension force in the string (T).
- Applied force (F_applied).
- Friction force between the penguin and the sled (F_ps).
- Friction force between the sled and the snow (F_snow).

Step 2: Determine the direction of each force.
- Tension force in the string acts in the horizontal direction opposite to the applied force.
- Applied force acts in the horizontal direction towards the right.
- The friction forces (F_ps and F_snow) act in the opposite direction to the motion.

Step 3: Calculate the friction forces.
- The friction force between the penguin and the sled is given by:
F_ps = μ_ps * normal force between the penguin and the sled.

- The friction force between the sled and the snow is given by:
F_snow = μ_snow * normal force between the sled and the snow.

Step 4: Find the normal forces.
- The normal force between the penguin and the sled is equal to the weight of the penguin:
Normal force between the penguin and the sled = m_penguin * g.

- The normal force between the sled and the snow is equal to the weight of the sled:
Normal force between the sled and the snow = m_sled * g.

Step 5: Calculate the friction forces using the obtained normal forces and coefficients of friction.
- F_ps = μ_ps * (m_penguin * g).
- F_snow = μ_snow * (m_sled * g).

Step 6: Apply Newton's second law.
- The sum of the forces in the horizontal direction is equal to the mass of the system multiplied by acceleration (F_net = m_total * a).
- The net force acting on the system is the difference between the applied force and the friction forces (F_net = F_applied - F_ps - F_snow).

Step 7: Solve for acceleration.
- Set up the equation from step 6 and solve for the acceleration.

Let's perform the calculations using the given values:
- m_penguin = 5.0 kg (mass of the penguin)
- m_sled = 12 kg (mass of the sled)
- F_applied = 45 N (applied force)
- μ_ps = 0.18 (coefficient of kinetic friction between the penguin and the sled)
- μ_snow = 0.14 (coefficient of kinetic friction between the sled and the snow)
- g = 9.8 m/s^2 (acceleration due to gravity)

We'll calculate the normal forces and friction forces. Then, we'll find the acceleration.

To solve this problem, we can use Newton's second law and the concept of friction.

First, let's determine the forces acting on the penguin-sled system:

1. Weight of the penguin (Wp) = mass of penguin (mp) × acceleration due to gravity (g).
Wp = 5.0 kg × 9.8 m/s² = 49 N

2. Weight of the sled (Ws) = mass of sled (ms) × acceleration due to gravity (g).
Ws = 12 kg × 9.8 m/s² = 117.6 N

3. Horizontal force applied to the sled (Fa) = 45 N.

4. Force of friction between the penguin and the sled (Fps) = coefficient of kinetic friction between them (μps) × normal force between them (Nps).
The normal force (Nps) is the force exerted by the sled on the penguin and is equal to the weight of the penguin (Wp).
Fps = μps × Wp

5. Force of friction between the sled and the snow (Fss) = coefficient of kinetic friction between them (μss) × normal force between them (Nss).
The normal force (Nss) is the force exerted by the snow on the sled and is equal to the weight of the sled (Ws).
Fss = μss × Ws

We need to find the tension in the string (T) that the penguin is holding onto to keep himself stationary. Since the penguin is not moving, the net force on the penguin-sled system in the horizontal direction is zero.

Net force in the horizontal direction = Fa - Fps - Fss - T = 0

Rearranging the equation:

T = Fa - Fps - Fss

Now, let's calculate Fps and Fss:

Fps = μps × Wp = 0.18 × 49 N = 8.82 N
Fss = μss × Ws = 0.14 × 117.6 N = 16.46 N

Substituting the values:

T = 45 N - 8.82 N - 16.46 N

T ≈ 19.72 N

Therefore, the tension in the string that the penguin is holding onto to keep himself stationary is approximately 19.72 N.

And, I wonder if the penguin has a question in this story, or not?