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When you hit a baseball, does the ball ever travel faster than the bat?
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It seems impossible, yet I'm thinking that maybe because the ball compresses against the bat a bit it acts a little like a spring, and DOES travel faster than the bat?
newtonian-mechanics momentum conservation-laws projectile sports
edited 52 mins ago
Qmechanic♦
97k121631034
asked 2 hours ago
Joshua Ronis
1018
add a comment |Â
up vote
2
down vote
favorite
It seems impossible, yet I'm thinking that maybe because the ball compresses against the bat a bit it acts a little like a spring, and DOES travel faster than the bat?
newtonian-mechanics momentum conservation-laws projectile sports
edited 52 mins ago
Qmechanic♦
97k121631034
asked 2 hours ago
Joshua Ronis
1018
It is momentum that is conserved and transferred, not speed. momentum=mv so a large mass hitting a small one and transferring its momentum must give it a larger speed , from conservation law.
– anna v
1 hour ago
When considering the mass of the bat, you'd also have to factor in the mass of the batter. That's part of the platform that is holding the bat.
– BillDOe
1 hour ago
Ever see a batter bunting the ball?
– Samuel Weir
1 hour ago
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
It seems impossible, yet I'm thinking that maybe because the ball compresses against the bat a bit it acts a little like a spring, and DOES travel faster than the bat?
newtonian-mechanics momentum conservation-laws projectile sports
edited 52 mins ago
Qmechanic♦
97k121631034
asked 2 hours ago
Joshua Ronis
1018
It seems impossible, yet I'm thinking that maybe because the ball compresses against the bat a bit it acts a little like a spring, and DOES travel faster than the bat?
newtonian-mechanics momentum conservation-laws projectile sports
newtonian-mechanics momentum conservation-laws projectile sports
edited 52 mins ago
Qmechanic♦
97k121631034
asked 2 hours ago
Joshua Ronis
1018
edited 52 mins ago
Qmechanic♦
97k121631034
asked 2 hours ago
Joshua Ronis
1018
edited 52 mins ago
Qmechanic♦
97k121631034
edited 52 mins ago
Qmechanic♦
97k121631034
edited 52 mins ago
Qmechanic♦
97k121631034
97k121631034
asked 2 hours ago
Joshua Ronis
1018
asked 2 hours ago
Joshua Ronis
1018
asked 2 hours ago
Joshua Ronis
1018
1018
It is momentum that is conserved and transferred, not speed. momentum=mv so a large mass hitting a small one and transferring its momentum must give it a larger speed , from conservation law.
– anna v
1 hour ago
When considering the mass of the bat, you'd also have to factor in the mass of the batter. That's part of the platform that is holding the bat.
– BillDOe
1 hour ago
Ever see a batter bunting the ball?
– Samuel Weir
1 hour ago
add a comment |Â
It is momentum that is conserved and transferred, not speed. momentum=mv so a large mass hitting a small one and transferring its momentum must give it a larger speed , from conservation law.
– anna v
1 hour ago
When considering the mass of the bat, you'd also have to factor in the mass of the batter. That's part of the platform that is holding the bat.
– BillDOe
1 hour ago
Ever see a batter bunting the ball?
– Samuel Weir
1 hour ago
It is momentum that is conserved and transferred, not speed. momentum=mv so a large mass hitting a small one and transferring its momentum must give it a larger speed , from conservation law.
– anna v
1 hour ago
It is momentum that is conserved and transferred, not speed. momentum=mv so a large mass hitting a small one and transferring its momentum must give it a larger speed , from conservation law.
– anna v
1 hour ago
When considering the mass of the bat, you'd also have to factor in the mass of the batter. That's part of the platform that is holding the bat.
– BillDOe
1 hour ago
When considering the mass of the bat, you'd also have to factor in the mass of the batter. That's part of the platform that is holding the bat.
– BillDOe
1 hour ago
Ever see a batter bunting the ball?
– Samuel Weir
1 hour ago
Ever see a batter bunting the ball?
– Samuel Weir
1 hour ago
add a comment |Â
3 Answers
3
active
oldest
votes
up vote
3
down vote
Yes. Consider throwing a ball at a bat which is held stationary: the ball is momentarily stationary but at all other times it is moving faster than the bat.
Now consider sweeping the bat towards an initially stationary ball: if the ball is not to stick to the bat, then it must be moving faster than it when it loses contact with it. (This case is identical to the one above with a different choice of reference frame of course.)
In neither of these cases have I taken proper account of conservation of momentum: the bat must change velocity slightly when it imparts momentum to the ball, so you can't hold it stationary or sweep it at a constant velocity in fact. But this change in velocity of the bat can be made as small as you like by making $m_textbat/m_textball$ large enough so the argument remains true.
answered 1 hour ago
tfb
13.2k32545
Note that the mass ratio is strictly controlled by the rules of baseball: balls at 0.145 kg, and bats at around 1 kg...
– DJohnM
1 hour ago
add a comment |Â
up vote
2
down vote
According to newton's third law of motion, both the base ball and the bat experience equal force but unequal acceleration which is because of different masses. If acceleration is different then velocity is also different for both ball and bat. So, ball would travel faster than the bat.
answered 1 hour ago
Ashika karikkalan
212
add a comment |Â
up vote
0
down vote
For an ideal heavy bat, the ball moves faster than its point of contact with the bat. Here's why.
- Suppose the bat is stationary and the ball comes in with velocity $-v$. Then since the bat is very heavy, it acts like an immovable wall and the ball bounces off elastically, getting velocity $+v$.
- Therefore, the change in velocity of the ball is precisely twice its relative velocity with the bat. By Galilean invariance, this is true in all reference frames, not just ones where the bat is stationary.
- Now suppose the batter is moving the bat with velocity $+w$. The relative velocity is now $v+w$, so the final velocity of the wall is
$$v_f = -v + 2(v + w) = v + 2w.$$
This is indeed always greater than the speed of the bat. For example, if you hit the ball from a tee, then $v_f = 2w$ so the baseball ends up going precisely twice as fast as the bat.
This can also be understood from a force perspective. If you think of the bat and ball as squishing during impact like tiny springs, then at the moment they're moving at the same speed $w$, there is a sizable amount of energy stored in the springs. As the collision ends, the springs release this energy, increasing the speed of the ball over that of the bat.
answered 1 hour ago
knzhou
34.1k897170
add a comment |Â
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
Yes. Consider throwing a ball at a bat which is held stationary: the ball is momentarily stationary but at all other times it is moving faster than the bat.
Now consider sweeping the bat towards an initially stationary ball: if the ball is not to stick to the bat, then it must be moving faster than it when it loses contact with it. (This case is identical to the one above with a different choice of reference frame of course.)
In neither of these cases have I taken proper account of conservation of momentum: the bat must change velocity slightly when it imparts momentum to the ball, so you can't hold it stationary or sweep it at a constant velocity in fact. But this change in velocity of the bat can be made as small as you like by making $m_textbat/m_textball$ large enough so the argument remains true.
answered 1 hour ago
tfb
13.2k32545
Note that the mass ratio is strictly controlled by the rules of baseball: balls at 0.145 kg, and bats at around 1 kg...
– DJohnM
1 hour ago
add a comment |Â
up vote
3
down vote
Yes. Consider throwing a ball at a bat which is held stationary: the ball is momentarily stationary but at all other times it is moving faster than the bat.
Now consider sweeping the bat towards an initially stationary ball: if the ball is not to stick to the bat, then it must be moving faster than it when it loses contact with it. (This case is identical to the one above with a different choice of reference frame of course.)
In neither of these cases have I taken proper account of conservation of momentum: the bat must change velocity slightly when it imparts momentum to the ball, so you can't hold it stationary or sweep it at a constant velocity in fact. But this change in velocity of the bat can be made as small as you like by making $m_textbat/m_textball$ large enough so the argument remains true.
answered 1 hour ago
tfb
13.2k32545
Note that the mass ratio is strictly controlled by the rules of baseball: balls at 0.145 kg, and bats at around 1 kg...
– DJohnM
1 hour ago
add a comment |Â
up vote
3
down vote
up vote
3
down vote
Yes. Consider throwing a ball at a bat which is held stationary: the ball is momentarily stationary but at all other times it is moving faster than the bat.
Now consider sweeping the bat towards an initially stationary ball: if the ball is not to stick to the bat, then it must be moving faster than it when it loses contact with it. (This case is identical to the one above with a different choice of reference frame of course.)
In neither of these cases have I taken proper account of conservation of momentum: the bat must change velocity slightly when it imparts momentum to the ball, so you can't hold it stationary or sweep it at a constant velocity in fact. But this change in velocity of the bat can be made as small as you like by making $m_textbat/m_textball$ large enough so the argument remains true.
answered 1 hour ago
tfb
13.2k32545
Yes. Consider throwing a ball at a bat which is held stationary: the ball is momentarily stationary but at all other times it is moving faster than the bat.
Now consider sweeping the bat towards an initially stationary ball: if the ball is not to stick to the bat, then it must be moving faster than it when it loses contact with it. (This case is identical to the one above with a different choice of reference frame of course.)
In neither of these cases have I taken proper account of conservation of momentum: the bat must change velocity slightly when it imparts momentum to the ball, so you can't hold it stationary or sweep it at a constant velocity in fact. But this change in velocity of the bat can be made as small as you like by making $m_textbat/m_textball$ large enough so the argument remains true.
answered 1 hour ago
tfb
13.2k32545
answered 1 hour ago
tfb
13.2k32545
answered 1 hour ago
tfb
13.2k32545
answered 1 hour ago
tfb
13.2k32545
13.2k32545
Note that the mass ratio is strictly controlled by the rules of baseball: balls at 0.145 kg, and bats at around 1 kg...
– DJohnM
1 hour ago
add a comment |Â
Note that the mass ratio is strictly controlled by the rules of baseball: balls at 0.145 kg, and bats at around 1 kg...
– DJohnM
1 hour ago
Note that the mass ratio is strictly controlled by the rules of baseball: balls at 0.145 kg, and bats at around 1 kg...
– DJohnM
1 hour ago
Note that the mass ratio is strictly controlled by the rules of baseball: balls at 0.145 kg, and bats at around 1 kg...
– DJohnM
1 hour ago
add a comment |Â
up vote
2
down vote
According to newton's third law of motion, both the base ball and the bat experience equal force but unequal acceleration which is because of different masses. If acceleration is different then velocity is also different for both ball and bat. So, ball would travel faster than the bat.
answered 1 hour ago
Ashika karikkalan
212
add a comment |Â
up vote
2
down vote
According to newton's third law of motion, both the base ball and the bat experience equal force but unequal acceleration which is because of different masses. If acceleration is different then velocity is also different for both ball and bat. So, ball would travel faster than the bat.
answered 1 hour ago
Ashika karikkalan
212
add a comment |Â
up vote
2
down vote
up vote
2
down vote
According to newton's third law of motion, both the base ball and the bat experience equal force but unequal acceleration which is because of different masses. If acceleration is different then velocity is also different for both ball and bat. So, ball would travel faster than the bat.
answered 1 hour ago
Ashika karikkalan
212
According to newton's third law of motion, both the base ball and the bat experience equal force but unequal acceleration which is because of different masses. If acceleration is different then velocity is also different for both ball and bat. So, ball would travel faster than the bat.
answered 1 hour ago
Ashika karikkalan
212
answered 1 hour ago
Ashika karikkalan
212
answered 1 hour ago
Ashika karikkalan
212
answered 1 hour ago
Ashika karikkalan
212
212
add a comment |Â
add a comment |Â
up vote
0
down vote
For an ideal heavy bat, the ball moves faster than its point of contact with the bat. Here's why.
- Suppose the bat is stationary and the ball comes in with velocity $-v$. Then since the bat is very heavy, it acts like an immovable wall and the ball bounces off elastically, getting velocity $+v$.
- Therefore, the change in velocity of the ball is precisely twice its relative velocity with the bat. By Galilean invariance, this is true in all reference frames, not just ones where the bat is stationary.
- Now suppose the batter is moving the bat with velocity $+w$. The relative velocity is now $v+w$, so the final velocity of the wall is
$$v_f = -v + 2(v + w) = v + 2w.$$
This is indeed always greater than the speed of the bat. For example, if you hit the ball from a tee, then $v_f = 2w$ so the baseball ends up going precisely twice as fast as the bat.
This can also be understood from a force perspective. If you think of the bat and ball as squishing during impact like tiny springs, then at the moment they're moving at the same speed $w$, there is a sizable amount of energy stored in the springs. As the collision ends, the springs release this energy, increasing the speed of the ball over that of the bat.
answered 1 hour ago
knzhou
34.1k897170
add a comment |Â
up vote
0
down vote
For an ideal heavy bat, the ball moves faster than its point of contact with the bat. Here's why.
- Suppose the bat is stationary and the ball comes in with velocity $-v$. Then since the bat is very heavy, it acts like an immovable wall and the ball bounces off elastically, getting velocity $+v$.
- Therefore, the change in velocity of the ball is precisely twice its relative velocity with the bat. By Galilean invariance, this is true in all reference frames, not just ones where the bat is stationary.
- Now suppose the batter is moving the bat with velocity $+w$. The relative velocity is now $v+w$, so the final velocity of the wall is
$$v_f = -v + 2(v + w) = v + 2w.$$
This is indeed always greater than the speed of the bat. For example, if you hit the ball from a tee, then $v_f = 2w$ so the baseball ends up going precisely twice as fast as the bat.
This can also be understood from a force perspective. If you think of the bat and ball as squishing during impact like tiny springs, then at the moment they're moving at the same speed $w$, there is a sizable amount of energy stored in the springs. As the collision ends, the springs release this energy, increasing the speed of the ball over that of the bat.
answered 1 hour ago
knzhou
34.1k897170
add a comment |Â
up vote
0
down vote
up vote
0
down vote
For an ideal heavy bat, the ball moves faster than its point of contact with the bat. Here's why.
- Suppose the bat is stationary and the ball comes in with velocity $-v$. Then since the bat is very heavy, it acts like an immovable wall and the ball bounces off elastically, getting velocity $+v$.
- Therefore, the change in velocity of the ball is precisely twice its relative velocity with the bat. By Galilean invariance, this is true in all reference frames, not just ones where the bat is stationary.
- Now suppose the batter is moving the bat with velocity $+w$. The relative velocity is now $v+w$, so the final velocity of the wall is
$$v_f = -v + 2(v + w) = v + 2w.$$
This is indeed always greater than the speed of the bat. For example, if you hit the ball from a tee, then $v_f = 2w$ so the baseball ends up going precisely twice as fast as the bat.
This can also be understood from a force perspective. If you think of the bat and ball as squishing during impact like tiny springs, then at the moment they're moving at the same speed $w$, there is a sizable amount of energy stored in the springs. As the collision ends, the springs release this energy, increasing the speed of the ball over that of the bat.
answered 1 hour ago
knzhou
34.1k897170
For an ideal heavy bat, the ball moves faster than its point of contact with the bat. Here's why.
- Suppose the bat is stationary and the ball comes in with velocity $-v$. Then since the bat is very heavy, it acts like an immovable wall and the ball bounces off elastically, getting velocity $+v$.
- Therefore, the change in velocity of the ball is precisely twice its relative velocity with the bat. By Galilean invariance, this is true in all reference frames, not just ones where the bat is stationary.
- Now suppose the batter is moving the bat with velocity $+w$. The relative velocity is now $v+w$, so the final velocity of the wall is
$$v_f = -v + 2(v + w) = v + 2w.$$
This is indeed always greater than the speed of the bat. For example, if you hit the ball from a tee, then $v_f = 2w$ so the baseball ends up going precisely twice as fast as the bat.
This can also be understood from a force perspective. If you think of the bat and ball as squishing during impact like tiny springs, then at the moment they're moving at the same speed $w$, there is a sizable amount of energy stored in the springs. As the collision ends, the springs release this energy, increasing the speed of the ball over that of the bat.
answered 1 hour ago
knzhou
34.1k897170
answered 1 hour ago
knzhou
34.1k897170
answered 1 hour ago
knzhou
34.1k897170
answered 1 hour ago
knzhou
34.1k897170
34.1k897170
add a comment |Â
add a comment |Â
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It is momentum that is conserved and transferred, not speed. momentum=mv so a large mass hitting a small one and transferring its momentum must give it a larger speed , from conservation law.
– anna v
1 hour ago
When considering the mass of the bat, you'd also have to factor in the mass of the batter. That's part of the platform that is holding the bat.
– BillDOe
1 hour ago
Ever see a batter bunting the ball?
– Samuel Weir
1 hour ago