When a 58 gram tennis ball is served, it accelerates from rest to a speed of 45 m/s. The impact with the racket gives the ball a constant acceleration over a distance of 44 cm. What is the magnitude of the net force acting on the ball?
m=58gm=0.058kg, u=0, V=45m/s, s=44cm=0.44m
so, v^2=u^2+2*a*s
a=2301.136m/s^2
F=ma
F=0.058*2301.136=133.466N
check it if correct
Well, let's serve up some physics humor! In this case, we can use Newton's second law, which states that force is equal to mass times acceleration (F = m * a). Since we are given the mass of the tennis ball (58 grams), we first need to convert it to kilograms (58 grams = 0.058 kg).
Next, we need to find the acceleration. We know that the ball starts from rest and reaches a speed of 45 m/s over a distance of 44 cm. To find the acceleration, we can use the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity (0 m/s), a is the acceleration, and s is the distance traveled.
Plugging in the values, we have (45 m/s)^2 = (0 m/s)^2 + 2 * a * 0.44 m. Solving for a, we get a = (45 m/s)^2 / (2 * 0.44 m) ≈ 513.75 m/s^2.
Now, we can calculate the magnitude of the net force using Newton's second law: F = m * a. Substituting the values, we get F = 0.058 kg * 513.75 m/s^2 ≈ 29.79 N.
So, the magnitude of the net force acting on the tennis ball is approximately 29.79 Newtons. That's a pretty smashing force if you ask me!
To find the magnitude of the net force acting on the ball, we can use Newton's second law of motion, which states that the net force (F_net) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a).
Given:
Mass of the tennis ball (m) = 58 grams = 0.058 kg
Final velocity of the ball (v) = 45 m/s
Distance over which the ball accelerates (s) = 44 cm = 0.44 m
To find the acceleration (a), we can use the equation:
v^2 = u^2 + 2as
Where:
v = final velocity
u = initial velocity (assumed to be zero, as the ball starts from rest)
a = acceleration
s = distance
Rearranging the equation, we get:
a = (v^2 - u^2) / (2s)
a = (45^2 - 0^2) / (2 * 0.44)
a = 1012.5 m/s^2
Now, we can calculate the magnitude of the net force (F_net) using Newton's second law:
F_net = m * a
F_net = 0.058 * 1012.5
F_net = 58.95 N
Therefore, the magnitude of the net force acting on the tennis ball is approximately 58.95 Newtons.
To find the magnitude of the net force acting on the ball, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Given:
- Mass of the ball (m) = 58 grams = 0.058 kg
- Final velocity of the ball (v) = 45 m/s
- Distance over which the acceleration occurs (d) = 44 cm = 0.44 m
First, we need to calculate the acceleration (a) of the ball using the kinematic equation:
v^2 = u^2 + 2ad
where u is the initial velocity (which is 0 in this case).
Substituting the given values:
45^2 = 0^2 + 2 * a * 0.44
2025 = 0.88a
a = 2025 / 0.88
a ≈ 2306.82 m/s^2
Now that we have the acceleration, we can use Newton's second law to find the net force (F).
F = m * a
Substituting the values:
F = 0.058 kg * 2306.82 m/s^2
F ≈ 133.77 N
Therefore, the magnitude of the net force acting on the ball is approximately 133.77 Newtons.