A person throws a 2.5 lb stone into the air with an initial upward speed of 15 ft/s. Make a free-body diagram for this stone (a) after it is free of the person’s hand and is traveling upward, (b) at its highest point, (c) when it is traveling down ward, and (d) while it is being thrown upward, but is still in contact with the person’s hand.
(a) After it is free of the person's hand and traveling upward, the free-body diagram for the stone would include gravity pointing downward (keeping it grounded), and an upward force due to the initial speed.
(b) At its highest point, the free-body diagram would show only the force of gravity acting downward since the stone momentarily stops moving upward.
(c) When it is traveling downward, the free-body diagram would show gravity acting downward and an additional force acting upward due to air resistance, making the stone feel slightly lighter.
(d) While it is being thrown upward but still in contact with the person's hand, the free-body diagram would include the force applied by the person's hand in the upward direction and gravity pointing downward. It's like playing a game of tug of war with gravity!
To make a free-body diagram for the stone at different stages, we need to consider the forces acting on it. Here's a breakdown for each scenario:
(a) After it is free of the person's hand and is traveling upward:
At this point, the stone is no longer in contact with the person's hand, and the forces acting on it are gravity and air resistance (neglecting any other external forces). Gravity pulls the stone downward, while air resistance acts in the opposite direction of its motion (upward). The free-body diagram will consist of the force of gravity pointing downward and the force of air resistance pointing upward.
(b) At its highest point:
At the highest point of its trajectory, the stone momentarily comes to rest before reversing direction. The forces acting on it are gravity pulling the stone downward (as in scenario (a)) and air resistance acting in the opposite direction of its motion (downward, as the stone is moving upward). The free-body diagram will show the force of gravity pointing downward and the force of air resistance pointing downward.
(c) When it is traveling downward:
When the stone is moving downward, the forces acting on it are gravity pulling it downward and air resistance acting in the opposite direction of its motion (upward). The free-body diagram will have the force of gravity pointing downward and the force of air resistance pointing upward, similar to scenario (a).
(d) While it is being thrown upward but is still in contact with the person's hand:
When the stone is being thrown upward and is still in contact with the person's hand, the forces acting on it are the force applied by the person's hand (upward), the force of gravity (pulling downward), and air resistance (neglecting any other external forces). The free-body diagram will include the force applied by the person's hand pointing upward, the force of gravity pointing downward, and the force of air resistance pointing upward.
Remember, the magnitude of air resistance can change depending on various factors such as the shape and size of the stone, its speed, and other environmental factors.