5 ms·

Could a styrofoam or other ball fall more slowly (like a feather) and therefore allow more of them to be thrown?

jcranmer 8y ago
The acceleration due to gravity is independent of mass. A 1cm ball made of lead and a 1cm ball made of wood would both fall at the same speed. What does make a difference is shape, due to differing amounts of air resistance and lift.
- tzs 8y ago
  The force from air resistance at a given velocity will be the same on the 1 cm lead ball and the 1 cm wood ball because they have the same shape and size. The acceleration from air resistance is the force divided by the mass, and so the 1 cm lead ball has much less acceleration from air resistance than does the 1 cm wood ball. As you note, the acceleration due to gravity is the same on both balls. The net acceleration, therefore, is larger for the 1 cm lead ball than for the 1 cm wood ball, and so the lead ball falls faster. The difference in acceleration between the lead ball and the wood ball might not be large enough to easily see if you just drop them a couple meters. Try a ping pong ball and a lead ball of the same diameter (4 cm). That lead ball would weigh 372 g. A ping pong ball is 2.7 g. At a given velocity, the acceleration from air resistance would be almost 140 times greater on the ping pong ball than on the lead ball. That should greatly reduce the height you need to drop from in order to see the difference.
  - ctchocula 8y ago
    This doesn't sound correct to me. The acceleration due to gravity is the same on both balls. However, since the lead ball weighs more than the wood ball, the force of gravity on the lead ball is stronger than the force on the wood ball (F_g = mg). The effect of air resistance can be modeled by a different force. It is typically modeled as a linear function of velocity rather than mass, and it models the behaviour that the faster an object is traveling the more it is affected by air resistance which acts in the opposite direction as the direction the object is traveling in (F_a = -kv). By adding the two forces together, you get a second-order differential equation that describes how the object behaves (F_g + F_a = F_net = ma). [1] https://oregonstate.edu/instruct/mth252h/Bogley/w02/resist.html https://oregonstate.edu/instruct/mth252h/Bogley/w02/resist.h...
    - tzs 8y ago
      > The effect of air resistance can be modeled by a different force. It is typically modeled as a linear function of velocity rather than mass [...] That's the key. The air resistance force is a function of velocity [1], and it is not a function of mass. Two bodies that are aerodynamically identical (same shape, size, same boundary interactions with the air) experience the same air resistance force at a given velocity, regardless of their masses. As you note, the falling body has two opposing forces. Gravity, which is proportional to the mass of the body, and air resistance, which depends on velocity and does not depend on mass. The motion of the body is determined by the net force. The net force on the ball is mg + D(v), where m is the mass of the ball, g is 9.81 m/s^2, and D(v) is the function that gives air resistance of the ball at velocity v. (Note: I'm using a coordinate system where balls fall in the positive direction. In this system D(v) will be negative). The net acceleration on the ball is net force divided by mass. This is g + D(v)/m. Note the effect of varying the mass, leaving all else the same. Remember, D(v) is negative, so the effect of the D(v)/m term is to reduce the net acceleration the ball feels. In other words, it is to make the ball fall slower. If we raise the mass, we reduce the magnitude of D(v)/m. We reduce the amount that air resistance slows down the ball. If we lower the mass, the opposite happens. Air resistance slows down the ball more. For a given ball, as it falls and picks up speed, the air resistance goes up, becoming more and more effective at countering the gravitation force. This puts an upper limit on how fast the ball can fall--the so-called "terminal velocity". This is the velocity where D(v) = -gm. Note that for balls with larger mass, terminal velocity will be higher. [1] a linear function at very low speed with no turbulence, a quadratic function in most situations we normally encounter in everyday life. The quadratic is 1/2 p Cd A v^2, where p is the density of the air, Cd is the drag coefficient (0.47 for a sphere), A is the cross sectional area, and v is the speed relative to the air.
      - ctchocula 8y ago
        You are correct only if all else is the same. However, I take issue with the assumption that you can leave all else the same. The net force on a heavier object is a higher for the lead ball than for the wood ball. The net force for the lead ball is m_l x a, but the net force on the wood ball is m_w x a where m_l>m_w, and the acceleration a depends on the shape of the object and can be thought of as the same.
jamiek88 8y ago
Galileo says no.
zw123456 8y ago
Or what about say a sort of balloon that is partially filled with helium such that is it just shy of neutral buoyancy, that would be like low gravity. Then perhaps a person could do 100's. Maybe.
ballenf 8y ago
What about an object with a one-way parachute of sorts change that? That is an object that rises at normal speed but falls at a fraction of the speed due to inherent aerodynamics? The effect would need to be super precise and air currents limited. And that may be impossible given all the motion going on.

The acceleration due to gravity is independent of mass. A 1cm ball made of lead and a 1cm ball made of wood would both fall at the same speed. What does make a difference is shape, due to differing amounts of air resistance and lift.

tzs 8y ago
The force from air resistance at a given velocity will be the same on the 1 cm lead ball and the 1 cm wood ball because they have the same shape and size. The acceleration from air resistance is the force divided by the mass, and so the 1 cm lead ball has much less acceleration from air resistance than does the 1 cm wood ball. As you note, the acceleration due to gravity is the same on both balls. The net acceleration, therefore, is larger for the 1 cm lead ball than for the 1 cm wood ball, and so the lead ball falls faster. The difference in acceleration between the lead ball and the wood ball might not be large enough to easily see if you just drop them a couple meters. Try a ping pong ball and a lead ball of the same diameter (4 cm). That lead ball would weigh 372 g. A ping pong ball is 2.7 g. At a given velocity, the acceleration from air resistance would be almost 140 times greater on the ping pong ball than on the lead ball. That should greatly reduce the height you need to drop from in order to see the difference.
- ctchocula 8y ago
  This doesn't sound correct to me. The acceleration due to gravity is the same on both balls. However, since the lead ball weighs more than the wood ball, the force of gravity on the lead ball is stronger than the force on the wood ball (F_g = mg). The effect of air resistance can be modeled by a different force. It is typically modeled as a linear function of velocity rather than mass, and it models the behaviour that the faster an object is traveling the more it is affected by air resistance which acts in the opposite direction as the direction the object is traveling in (F_a = -kv). By adding the two forces together, you get a second-order differential equation that describes how the object behaves (F_g + F_a = F_net = ma). [1] https://oregonstate.edu/instruct/mth252h/Bogley/w02/resist.html https://oregonstate.edu/instruct/mth252h/Bogley/w02/resist.h...
  - tzs 8y ago
    > The effect of air resistance can be modeled by a different force. It is typically modeled as a linear function of velocity rather than mass [...] That's the key. The air resistance force is a function of velocity [1], and it is not a function of mass. Two bodies that are aerodynamically identical (same shape, size, same boundary interactions with the air) experience the same air resistance force at a given velocity, regardless of their masses. As you note, the falling body has two opposing forces. Gravity, which is proportional to the mass of the body, and air resistance, which depends on velocity and does not depend on mass. The motion of the body is determined by the net force. The net force on the ball is mg + D(v), where m is the mass of the ball, g is 9.81 m/s^2, and D(v) is the function that gives air resistance of the ball at velocity v. (Note: I'm using a coordinate system where balls fall in the positive direction. In this system D(v) will be negative). The net acceleration on the ball is net force divided by mass. This is g + D(v)/m. Note the effect of varying the mass, leaving all else the same. Remember, D(v) is negative, so the effect of the D(v)/m term is to reduce the net acceleration the ball feels. In other words, it is to make the ball fall slower. If we raise the mass, we reduce the magnitude of D(v)/m. We reduce the amount that air resistance slows down the ball. If we lower the mass, the opposite happens. Air resistance slows down the ball more. For a given ball, as it falls and picks up speed, the air resistance goes up, becoming more and more effective at countering the gravitation force. This puts an upper limit on how fast the ball can fall--the so-called "terminal velocity". This is the velocity where D(v) = -gm. Note that for balls with larger mass, terminal velocity will be higher. [1] a linear function at very low speed with no turbulence, a quadratic function in most situations we normally encounter in everyday life. The quadratic is 1/2 p Cd A v^2, where p is the density of the air, Cd is the drag coefficient (0.47 for a sphere), A is the cross sectional area, and v is the speed relative to the air.
    - ctchocula 8y ago
      You are correct only if all else is the same. However, I take issue with the assumption that you can leave all else the same. The net force on a heavier object is a higher for the lead ball than for the wood ball. The net force for the lead ball is m_l x a, but the net force on the wood ball is m_w x a where m_l>m_w, and the acceleration a depends on the shape of the object and can be thought of as the same.

jamiek88 8y ago

Galileo says no.

zw123456 8y ago

Or what about say a sort of balloon that is partially filled with helium such that is it just shy of neutral buoyancy, that would be like low gravity. Then perhaps a person could do 100's. Maybe.

ballenf 8y ago

What about an object with a one-way parachute of sorts change that? That is an object that rises at normal speed but falls at a fraction of the speed due to inherent aerodynamics? The effect would need to be super precise and air currents limited. And that may be impossible given all the motion going on.