Question

a balloon is waiting to take off. as seen in the figure below, the balloons basket sits on a platform which rests on the ground. the balloon is pulling up on the basket, but not hard enough to lift it off the platform. what is the free - body diagram for the plat - form? some parallel vectors are offset hori - zontally for clarity.

Explanation:

Step1: Analyze forces on platform

The platform has three forces acting on it. The gravitational force \(F_{grav\ on\ plat}\) pulling it down. The upward force from the ground \(F_{ground\ on\ plat}\). And the downward force from the basket \(F_{bask\ on\ plat}\) (which is equal in magnitude to the normal force the platform exerts on the basket, but in the opposite direction).

Step2: Check each option

• Option1: Forces on basket are shown, not platform. Incorrect.
• Option2: \(F_{ground\ on\ plat}\) (up), \(F_{grav\ on\ plat}\) (down), \(F_{bask\ on\ plat}\) (down). Correct as these are the forces on the platform.
• Option3: \(F_{bal\ on\ plat}\) is incorrect. The balloon pulls on the basket, not directly on the platform. Incorrect.
• Option4: Forces related to platform - basket and platform - ground interactions are mis - represented. Incorrect.
• Option5: \(F_{bal\ on\ plat}\) is incorrect. The balloon pulls on the basket, not directly on the platform. Incorrect.

Answer:

1. \(F_{ground\ on\ plat}\) (up), \(F_{grav\ on\ plat}\) (down), \(F_{bask\ on\ plat}\) (down)