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







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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














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







share|cite|improve this question























  • 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












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







share|cite|improve this question















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






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edited 52 mins ago









Qmechanic♦

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asked 2 hours ago









Joshua Ronis

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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
















  • 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










3 Answers
3






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3
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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.






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  • 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

















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.






share|cite|improve this answer



























    up vote
    0
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    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.






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      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.






      share|cite|improve this answer




















      • 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














      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.






      share|cite|improve this answer




















      • 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












      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.






      share|cite|improve this answer












      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.







      share|cite|improve this answer












      share|cite|improve this answer



      share|cite|improve this answer










      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
















      • 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










      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.






      share|cite|improve this answer
























        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.






        share|cite|improve this answer






















          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.






          share|cite|improve this answer












          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.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 1 hour ago









          Ashika karikkalan

          212




          212




















              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.






              share|cite|improve this answer
























                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.






                share|cite|improve this answer






















                  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.






                  share|cite|improve this answer












                  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.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 1 hour ago









                  knzhou

                  34.1k897170




                  34.1k897170



























                       

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