While sitting in a lounge chair with the back inclined at an angle of 10 degrees from the vertical, you tuck a pillow between your head and the chair. Then you lower the chair back to 40 degrees and doze with the pillow in place. How has the net force on the pillow changed?
the key is "net force".
in both cases acceleration is zero. therefore net force is also zero. Newton's second law, Fnet = mass * accel
Less compression in your neck and more weight of your head on the pillow.
To determine how the net force on the pillow has changed, we need to analyze the forces acting on the pillow in both positions - when the back of the chair is inclined at 10 degrees and when it is lowered to 40 degrees.
In the initial position, when the back of the chair is inclined at 10 degrees, we have the following forces acting on the pillow:
1. Weight (W): This force acts vertically downward due to the gravitational pull on the pillow.
2. Normal force (N): This force acts perpendicular to the surface of the chair, pushing the pillow upward.
3. Friction force (F): This force acts parallel to the surface of the chair, opposing the motion of the pillow.
Now, when you tuck the pillow between your head and the chair, the net force on the pillow in this position is zero since the normal force and the friction force balance out the weight.
Next, when you lower the chair back to 40 degrees, the forces acting on the pillow will be:
1. Weight (W): This force still acts vertically downward.
2. Normal force (N): This force acts perpendicular to the surface of the chair, pushing the pillow upward.
3. Friction force (F): This force acts parallel to the surface of the chair, opposing the motion of the pillow.
In this new position, the net force on the pillow will still be zero since the normal force and the friction force balance out the weight.
Therefore, the net force on the pillow does not change as you lower the chair back to 40 degrees while the pillow is in place.
To understand how the net force on the pillow has changed, let's break down the forces acting on the pillow in each situation.
When sitting in a lounge chair with the back inclined at an angle of 10 degrees from the vertical, there are three main forces acting on the pillow:
1. Gravity: This force pulls the pillow downward, towards the ground.
2. Normal force: This force is exerted by the chair on the pillow and acts perpendicular to the surface of the chair. It counteracts the force of gravity.
3. Friction: If there is any friction between the pillow and the back of the chair, it will act parallel to the surface of the chair and oppose any motion or sliding of the pillow.
Now, when you lower the chair back to 40 degrees and doze with the pillow in place, the forces acting on the pillow change as follows:
1. Gravity: This force still pulls the pillow downward, towards the ground. It remains unchanged.
2. Normal force: The normal force now acts perpendicular to the new inclined surface of the chair. As the incline angle has increased from 10 degrees to 40 degrees, the normal force will be smaller compared to the previous situation. This is because the greater the incline, the smaller the component of the normal force that counteracts gravity.
3. Friction: The friction force will also be affected by the increased incline angle. Friction acts parallel to the surface of the chair. With an increased incline angle of 40 degrees, the friction force will be stronger compared to the previous situation with a 10-degree incline.
In summary, the net force on the pillow decreases due to a reduction in the normal force and increases due to an increase in the friction force as the chair's back incline angle changes from 10 degrees to 40 degrees.