Problem 28 - College Physics

Question

A person throws a 2.5 lb stone into the air with an initial upward speed of 15 \(\mathrm{ft} / \mathrm{s}\) . 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 downward, and (d) while it is being thrown upward, but is still in contact with the person's hand.

Step-by-Step Solution

Answer

The only force when free of hand is gravity; while in hand, gravity and applied force act.

Step 1: Understand Forces on an Object Out of Hand Going Upward

When the stone is traveling upward after being released, the only force acting on it is gravity, which pulls it downward. There are no other forces in play since air resistance is typically neglected in such problems. In the free-body diagram, represent the stone with a dot and draw an arrow pointing downward labeled with the force due to gravity (weight).

Step 2: Understand Forces at the Highest Point

At the stone's highest point, it has no vertical motion (momentarily), but gravity is still acting on it. Hence, even when the velocity is zero, the force of gravity is still present. In the free-body diagram, represent the stone as a dot with a single downward arrow indicating the gravitational force.

Step 3: Understand Forces on an Object Traveling Downward

As the stone travels downward after reaching its peak, gravity continues to be the sole force acting on it, pulling it downward. In the free-body diagram, represent the stone with a dot and draw an arrow pointing downward corresponding to the gravitational force.

Step 4: Understand Forces While Still in Contact with the Hand

While the stone is being thrown and is still in contact with the person's hand, two forces act on it: the force exerted by the hand pushing it up and gravity pulling it down. In the free-body diagram, represent the stone with a dot, then draw an upward arrow representing the force exerted by the hand and a downward arrow for gravity.

Key Concepts

Gravity

Gravity is a force that pulls objects towards the center of the Earth. All objects with mass experience this force, and it acts constantly, whether the object is moving, stationary, or temporarily stopped.

• Gravity is the reason a thrown stone will eventually fall back to the ground after being tossed upwards.
• Its magnitude depends on the mass of the object and the gravitational constant, which is approximately 9.81 m/s² on Earth.

When creating a free-body diagram, gravity is typically represented by a single arrow pointing downward from the object. For example, when the stone reaches its highest point and stops momentarily, gravity is the only force acting on it, pulling it back down.

Force

Force is any interaction that changes the motion or shape of an object. It is typically measured in newtons (N).

• Forces can be applied in a variety of directions, and they are vectors, meaning they have both magnitude and direction.
• In physics problems like throwing a stone, understanding forces helps us predict motion.

While the stone is still in the person's hand, two forces are involved: the upward force exerted by the hand and the downward force of gravity. This is depicted in a free-body diagram using an upward arrow for the hand force and a downward arrow for gravity. This illustrates how different forces can affect the stone's motion simultaneously.

Motion

Motion is the change in position of an object over time. In physics, understanding the different forces involved helps to predict the future position, speed, and direction of an object.

• When the stone is thrown upwards, its motion is initially upward until gravity slows it down.
• At the highest point, the stone momentarily stops before gravity causes it to move downward again.
• Thus, motion is not only about movement but also about changes and transitions between states of movement.

In the stone's ascent, you can visually identify changes in speed and direction in a free-body diagram, emphasizing the simplicity with which such movements are analyzed in basic physics.

Projectile

A projectile is any object that moves through space upon its release. Once thrown or launched, it is only subject to gravity and air resistance, which in simple cases like this is often ignored.

• Gravitational force remains the only significant force acting on it during its flight post-launch.
• The parabolic path of a projectile, like the stone, is due to the gravitational force's constant downward pull.

When constructing a projectile's free-body diagram at different stages (upward, highest point, downward), the continuous influence of gravity is apparent. Observing these diagrams highlights the trajectory and helps visualize the path the object follows through air, simplifying the complex movement for analysis and understanding in physics.