Conceptual Physics

Variables

What is the strategy?

1. Draw a free-body diagram.


2. Use trigonometry to calculate the net force on the ball along each axis.


3. Use Newton’s second law to find the acceleration of the ball along each axis. The mass of the ball is not given, but you can determine it
   because you are told its weight. We do this in the variables table.

Physics principles and equations

Newton’s second law

ȈF = ma

Step-by-step solution

We begin by calculating the net force along the x axis.

We next calculate the force along the y axis. In this case, there are two forces to consider.

Now we calculate the acceleration along the x axis, using Newton’s second law.

We calculate the acceleration along the y axis.

The acceleration values may seem very large, but this is the acceleration during the brief moment the bat is in contact with the ball.

x component y component

weight 0 mg sin 270° = í1.40 N

force F cosș F sinș

acceleration ax ay

force F = 262 N

angle ș = 60.0°

mass m = mg/g = (1.40 N) / (9.80 m/s^2 ) = 0.143 kg

Step Reason

1. ȈFx = F cos ș net force along x axis

2. ȈFx = (262 N)(cos 60.0°) x component of force

3. ȈFx = 131 N evaluate

Step Reason

4. ȈFy = F sin ș + (í1.40 N) net force along y axis

5. enter values

6. ȈFy = 225 N evaluate

Step Reason

7. ȈFx = max Newton's second law

8. ax =ȈFx/m solve for ax

9. ax = (131 N) / (0.143 kg) enter values from step 3 and table

10.ax = 916 m/s^2 division

Step Reason

11.ȈFy = may Newton's second law

12.ay =ȈFy/m solve for ay

13.ay = (225 N)/(0.143 kg) enter values from step 6, table

14.ay = 1570 m/s^2 division

(^106) Copyright 2007 Kinetic Books Co. Chapter 05