Ladder safety
If a ladder rests inclined against a wall, would it be safer if the floor was frictionless and the wall was rough or if the wall was frictionless and the floor was rough?
Answer
The force of friction depends on the coefficient of friction and the normal force. In this situation, we'll assume that the coefficients are equal, which means that the setup that involves a greater normal force will create a stronger frictional force.
What is it that creates the normal force? Gravity pulls the ladder down, and the floor and wall provide normal forces. If the ladder is mostly upright, the normal force from the floor has to provide most of the vertical force opposing gravity, so we would expect the force of friction with the floor to be greater. What does that tell you about the safety?
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The force of friction depends on the coefficient of friction and the normal force. In this situation, we'll assume that the coefficients are equal, which means that the setup that involves a greater normal force will create a stronger frictional force.
What is it that creates the normal force? Gravity pulls the ladder down, and the floor and wall provide normal forces. If the ladder is mostly upright, the normal force from the floor has to provide most of the vertical force opposing gravity, so we would expect the force of friction with the floor to be greater. What does that tell you about the safety?