A ball is thrown straight up into the air. At each of the following instants, is the magnitude of the ball's acceleration greater than g, equal to g, less than g, or zero? Air resistance may be neglected.
A) just after leaving your hand?
B) at the very top (maximum height)?
C) just before hitting the ground?
the acceleration is always g, as the force on the ball from earth is constant.
g is g is g
A) just after leaving your hand:
The magnitude of the ball's acceleration is greater than g. This is because just after leaving your hand, the ball is accelerating upwards due to the force of your throw, and gravity is also acting downwards. The net acceleration is the sum of these accelerations, which is greater than g.
B) at the very top (maximum height):
The magnitude of the ball's acceleration is zero. At the maximum height, the ball momentarily stops moving upwards and starts moving downwards. Hence, for an instant, the velocity of the ball is zero, and hence the acceleration is also zero.
C) just before hitting the ground:
The magnitude of the ball's acceleration is greater than g. Just before hitting the ground, the ball is accelerating downwards due to the force of gravity. Since the acceleration due to gravity is constant and always acting downwards, the magnitude of the ball's acceleration is equal to g.
To determine the magnitude of the ball's acceleration at different instants, we need to understand that the acceleration of an object is determined by the forces acting on it. In this case, the main force acting on the ball is gravity, which is pulling it downward with an acceleration of g (approximately 9.8 m/s²).
A) Just after leaving your hand:
At this instant, the only force acting on the ball is gravity pulling it downward. Since there are no other forces counteracting gravity, the acceleration of the ball will be equal to the acceleration due to gravity (g). Therefore, the magnitude of the ball's acceleration is equal to g.
B) At the very top (maximum height):
At the highest point of its trajectory, the velocity of the ball becomes momentarily zero. However, gravity is still acting on the ball, trying to pull it downward. Therefore, the ball's acceleration at this instant is equal to g since gravity is the only force acting on it.
C) Just before hitting the ground:
As the ball descends towards the ground, gravity continues to act on it. However, in addition to gravity, the ground exerts an upward force (normal force) on the ball to support its weight. This results in a net force acting in the opposite direction to gravity. Consequently, the magnitude of the ball's acceleration just before hitting the ground will be less than g.
In summary:
A) just after leaving your hand: magnitude of acceleration = g
B) at the very top (maximum height): magnitude of acceleration = g
C) just before hitting the ground: magnitude of acceleration < g