Background: The sloping surface of the inclined plane supports part of the weight of the object as it moves up the slope. As a result, it takes less force to move the object uphill. The trade-off is that the object must be moved over a greater distance than if it were moved straight up to the higher elevation. On the other hand, the output force is greater than the input force because it is applied over a shorter distance. Like other simple machines, the ideal mechanical advantage of an inclined plane is given by

Situation: Sam is moving construction materials into a new home he is building. The stairs to the second floor of the home have not yet been built, so he needs to build a ramp to get the materials to the second floor. Sam is trying to decide between two ramp options for moving the supplies: Ramp A has a small slope but is longer than Ramp B; Ramp B has a steep slope but is shorter than Ramp A.

Question: Which ramp will require less force to move the supplies to the second floor?

Situation: Sam is moving construction materials into a new home he is building. The stairs to the second floor of the home have not yet been built, so he needs to build a ramp to get the materials to the second floor. Sam is trying to decide between two ramp options for moving the supplies: Ramp A has a small slope but is longer than Ramp B; Ramp B has a steep slope but is shorter than Ramp A.

Question: Which ramp will require more force to move the supplies to the second floor?

Situation: Sam is moving construction materials into a new home he is building. The stairs to the second floor of the home have not yet been built, so he needs to build a ramp to get the materials to the second floor. Sam is trying to decide between two ramp options for moving the supplies: Ramp A has a small slope but is longer than Ramp B; Ramp B has a steep slope but is shorter than Ramp A.

Question: Will Ramp A require more or less force to move the supplies than Ramp B?

Situation: Sam is moving construction materials into a new home he is building. The stairs to the second floor of the home have not yet been built, so he needs to build a ramp to get the materials to the second floor. Sam is trying to decide between two ramp options for moving the supplies: Ramp A has a small slope but is longer than Ramp B; Ramp B has a steep slope but is shorter than Ramp A.

Question: Will Ramp B require more or less force to move the supplies than Ramp A?

Situation: Sam is moving construction materials into a new home he is building. The stairs to the second floor of the home have not yet been built, so he needs to build a ramp to get the materials to the second floor. Sam is trying to decide between two ramp options for moving the supplies: Ramp A has a small slope but is longer than Ramp B; Ramp B has a steep slope but is shorter than Ramp A.

Question: Which ramp will require the supplies to be moved over a greater distance?

Situation: Sam is moving construction materials into a new home he is building. The stairs to the second floor of the home have not yet been built, so he needs to build a ramp to get the materials to the second floor. Sam is trying to decide between two ramp options for moving the supplies: Ramp A has a small slope but is longer than Ramp B; Ramp B has a steep slope but is shorter than Ramp A.

Question: Which ramp will require the supplies to be moved over a shorter distance?

Situation: Marty and Joe are moving furniture into Joe's new house. The house needs a lot of repair work, and the stairs to the second floor of the home are currently broken. Marty thinks it would be better to use a ramp with a slight incline to move Joe's furniture from the first floor to the second floor. Joe disagrees and thinks it would be faster and easier to just use a ladder in a completely vertical position to move the furniture straight up from the first floor to the second floor.

Question: Will it take more or less force to move the furniture using the ramp?

Situation: Marty and Joe are moving furniture into Joe's new house. The house needs a lot of repair work, and the stairs to the second floor of the home are currently broken. Marty thinks it would be better to use a ramp with a slight incline to move Joe's furniture from the first floor to the second floor. Joe disagrees and thinks it would be faster and easier to just use a ladder in a completely vertical position to move the furniture straight up from the first floor to the second floor.

Question: Will it take more or less force to move the furniture using the  ladder?