In t-ball, young players use a bat to hit a stationary ball off a stand. The 140 g ball has about the same mass as a baseball, but it is larger and softer. In one hit, the ball leaves the bat at 12 m/s after being in contact with the bat for 2.0 ms . Assume constant acceleration during the hit. a.What is the acceleration of the ball? Express your answer to two significant figures and include the appropriate units. a =
b. What is the net force on the ball during the hit?

Express your answer to two significant figures and include the appropriate units.

F =

The acceleration is

The net force on the ball during the hit is  

Explanation:

In order to gain a good understanding of the solution above we need to understated that the main concept used to solve this problem is Newton’s First and Second law .

Initially, calculate the change in momentum of the ball. Later, compare the expression for force to find the acceleration of ball. Finally, change in momentum is equivalent to the force experienced by the ball.

Now looking at the fundamentals

  Newton’s second law of motion in terms of momentum is as follows,

Here, is change in momentum, is change in time, m is mass and a is acceleration.

Momentum is given by the following formula,

Here, p is momentum, mm is mass and v is velocity.

The net force on the ball during the hit is given by

Here F is the force, m is the mass and a is the acceleration

Step One

Calculate change in momentum.

Is final velocity of ball and is initial velocity of ball.

Substitute, 12 for 0 for and 140 for m

Now consider the following expression,

Rearrange the above expression for acceleration.

Substitute, for , for and for m .

The acceleration of the ball

Note :

Initially ball was in rest so, initial velocity is . Om the last line of calculation the term and in the denominator is multiplied to convert and respectively into SI units.

Step Two

Rate of change in momentum is as follows,

Substitute, for and for .

Hence the net force on the charge is  840 N

Note :

From second law of motion force is equivalent to the rate of change of momentum.

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.