When a 57.0 gram tennis ball is served, it accelerates from rest to a speed of 46.5 m/s. The impact with the racket gives the ball a constant acceleration over a distance of 44.8 cm. What is the magnitude of the net force acting on the ball in newtons?
V^2 = Vo^2 + 2a*d
a = (V^2-Vo^2)/2d
a = (46.5^2-0)/89.6 = 24.13 m/s^2
F = m*a = 57 * 24.13 = 1376 N.
To find the magnitude of the net force acting on the tennis ball, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
First, let's convert the mass of the tennis ball from grams to kilograms. We divide 57.0 grams by 1000 to get 0.057 kilograms.
Next, we can find the acceleration of the tennis ball using the kinematic equation:
v^2 = u^2 + 2as
where:
- v is the final velocity (46.5 m/s),
- u is the initial velocity (0 m/s since it starts from rest),
- a is the acceleration, and
- s is the distance over which the acceleration occurs (44.8 cm or 0.448 meters).
Rearranging the equation:
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = (46.5^2 - 0^2) / (2 * 0.448)
Calculating the acceleration gives us a value of 240.796 m/s².
Finally, we can find the net force by multiplying the mass and acceleration:
Net force = mass * acceleration
= 0.057 kg * 240.796 m/s²
By calculating the multiplication, we find that the magnitude of the net force acting on the tennis ball is approximately 13.75 Newtons.