What is the Terminal Velocity of a Ball Dropped from a Height?
When an object is dropped, it accelerates downwards due to gravity. However, the force of air resistance acts against this acceleration, slowing the object down. Eventually, the force of air resistance becomes equal to the force of gravity, and the object reaches its terminal velocity. This is the constant speed at which the object continues to fall until it hits the ground.
The terminal velocity of an object depends on its mass, shape, and density, as well as the density of the surrounding medium. For example, a small, dense object like a ball bearing will have a higher terminal velocity than a large, less dense object like a balloon. The terminal velocity of an object also increases as the density of the surrounding medium decreases. For example, an object falling through water will have a lower terminal velocity than an object falling through air.
The terminal velocity of a ball dropped from a height can be calculated using the following formula:
v_t = sqrt(2mg / ρAC_d)
where:
- v_t is the terminal velocity
- m is the mass of the ball
- g is the acceleration due to gravity
- ρ is the density of the surrounding medium
- A is the cross-sectional area of the ball
- C_d is the drag coefficient
Related Questions
- What factors affect the terminal velocity of a ball? Mass, shape, density, and density of the surrounding medium.
- What is the terminal velocity of a ball falling through air at sea level? Approximately 9.8 m/s.
- What is the terminal velocity of a ball falling through water? Approximately 1.1 m/s.
- Can the terminal velocity of an object be greater than the speed of sound? Yes, if the object is falling through a medium with a higher density than air.
- What is the shape of an object that has the highest terminal velocity? A sphere.
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