course phy 201 9 7/16 025. `query 25
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Given Solution: `a** Gravity exerts a downward force equal to the weight of the ball. While in contact with the ball, and only while i contact, the bat exerts a normal force, which pushes outward along a line originating from the central axis of the bat. This force is perpendicular to the surface of the bat at the point of contact. Unless the direction of the ball is directly toward the center of the bat, which will not be the case if the ball is hit at an upward angle by a nearly level swing, there will also be a frictional force between bat and ball. This frictional force will be parallel to the surface of the bat and will act on the ball in the 'forward' direction. COMMON STUDENT ERROR: The gravitational force and the force exerted by the ball on the bat are equal and opposite. The force of the bat on the ball and the gravitational force are not equal and opposite, since this is not an equilibrium situation--the ball is definitely being accelerated by the net force, so the net force is not zero. ** COMMON STUDENT ERROR: Confusing motion in a direction with force in that direction. There is no force associated with the motion of the ball. The velocity of the ball in will remain unchanged if there is no net force on the ball. Furthermore, if the is net force has zero component in the x direction, the x velocity remains unchanged; the analogous statement holds for the y direction. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok Self-critique Rating:ok ********************************************* Question: `qgen phy list the forces on the ball while flying toward the outfield, and describe the directions of these forces YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: gravity, air resistance gravity is constant, air resistance depends on the speed of ball Confidence rating: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a**After impact the forces are gravity, which is constant and in the y direction, and air resistance. The direction of the force of air resistance is opposite to the direction of motion. The direction of motion is of course constantly changing, and the magnitude of the force of air resistance depends on the speed of the ball with respect to the air, which is also changing. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok Self-critique Rating:ok ********************************************* Question: `qgen phy give the source of each force you have described YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: gravity is a normal force between the ball and the earth frictional force is also a normal force between the bat and the ball Confidence rating: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** The gravitational force is the result of the gravitational attraction between the ball and the Earth. The normal force is the result of the elastic compression of bat and ball. The frictional force is due to a variety of phenomena related to the tendency of the surfaces to interlock (electromagnetic forces are involved) and to encounter small 'bumps' in the surfaces. ** ERRONEOUS STUDENT ANSWER: the air, the pitcher, the bat/ batter. friction. gravity INSTRUCTOR RESPONSE: All these are sources of force in one or both situations (bat striking ball, ball flying toward outfield) except the pitcher. The pitcher exerted a force previously, and that force was instrumental in delivering the ball to the batter, but that force ended well before any of these events occurred. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok Self-critique Rating: ok ********************************************* Question: `qgen phy what is the direction of the net force on the ball while in contact with the bat? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: gravity and friction remain constant Confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** We assume that the y axis is directed vertically upward, and the x axis is horizontal. The normal force will vary from 0 at the instant contact begins to a maximum at the instant of greatest compression, and back to 0 at the instant contact ceases. So there is no single normal force. However we can represent 'the' normal force as the average normal force. The gravitational force will remain constant. The frictional force will vary along with the normal force, and we will speak here of the average frictional force. The average normal force will be the greatest of these forces, much greater than friction or gravity. The frictional force will likely also exceed the gravitational force. The y component of the normal force will overwhelm the y components of the frictional force and the gravitational force, both of which are downward, giving us a net y component slightly less than the y component of the normal force. The x component of the normal force will be reinforced by the x component of the frictional force, making the x component of the net force a bit greater than the x component of the normal force. This will result in a net force that is 'tilted' forward and slightly down from the normal force. Note that the frictional force will tend to 'spin' the baseball but won't contribute much to the translational acceleration of the ball. This part is a topic for another chapter. ** IMPORTANT NOTE: It is essential that you sketch a diagram showing these forces. You are very unlikely to understand the explanation given here without a picture. Even with a picture this might be challenging. If you are not sure you understand, you should submit a copy of this question and solution, along your questions and/or commentary (mark insertions with ****). STUDENT COMMENT: Not sure about the frictional force. Why is it down? How do we calculate it? INSTRUCTOR RESPONSE: The frictional force exerted on the ball by the bat is perpendicular to the normal force, so the frictional force is exerted in the plane tangent to both the ball and the bat (imagine a flat piece of cardboard sandwiched between the ball and the bat; it lies in this tangent plane. If you have a line segment connecting the middle of the ball with the middle of the bat, it is perpendicular to the tangent plane (this line segment would cut through the piece of carboard at a right angle). Note that the direction of the normal force on the ball is along this line.). It is clear that the x component of the frictional force on the ball is in the 'forward' direction of motion. It is also clear that the in the tangent plane, the 'forward' direction is also downward. So the frictional force has a positive x component, and a negative y component. Assuming the ball does not 'slip' in contact with the bat, the frictional force is the force of static friction. The force of static friction cannot exceed the product of the coefficient of friction and the normal force: f_static < = mu * N, where f_static is the force of static friction, mu is the coefficient of static friction and N is the normal force. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok Self-critique Rating:ok ********************************************* Question: `qgen phy what is the net force on the ball while flying toward the outfield? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: downward gravitational force and air resistance Confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** The net force will consist of the downward gravitational force and the force of air resistance opposing the motion. If the ball is rising the y component of the air resistance will be in the downward direction, reinforcing the gravitational force and giving a net downward y component slightly exceeding that of gravity. If the ball is falling the y component will be in the upward direction, opposing the gravitational force and giving a net downward y component slightly less than that of gravity. In either case the x component will be in the direction opposite to the motion of the ball, so the net force will be directed mostly downward but also a bit 'backward'. There are also air pressure forces related to the spinning of the ball; the net force exerted by air pressure causes the path of the ball to curve a bit, but these forces won't be considered here. ** Self-critique (if necessary):ok Self-critique Rating:ok "