I am an idiot, me. (Find the force of a tennis ball)

[Blablablabla]

This seems like such a pathetically elementary problem, and I feel like a total moron right now. Well, here it is:


When a 58 gram tennis ball is served, it accelerates from rest to a speed of 45 m/s. The impact of 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?



The answer is 130 N. The only force formula I know is f=ma. I know that the distance (44 cm) is supposed to be used, and maybe gravity (9.8 m/s²) should be considered but I have no clue how. Thanks for any help :(

 

[SammyS]

This seems like such a pathetically elementary problem, and I feel like a total moron right now. Well, here it is:

When a 58 gram tennis ball is served, it accelerates from rest to a speed of 45 m/s. The impact of 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?

The answer is 130 N. The only force formula I know is f=ma. I know that the distance (44 cm) is supposed to be used, and maybe gravity (9.8 m/s²) should be considered but I have no clue how. Thanks for any help :(

Why would acceleration of gravity have anything to do with this? It doesn't.

Do you know how the work done on an object is related to the object's change in kinetic energy?

 

[HallsofIvy]

SammyS's suggestion that you look at the change in energy, the work done by the racket, is probably the simplest way to do this.

However, since you say "The only force formula I know is f=ma", you can do it that way. With a constant acceleration, a, and initial speed 0, the speed after the acceleration is v= at and the total distance moved would be (1/2)at^2. You know, then, that at= 45 m/s and (1/2)at^2= .44 m. You can solve the first equation for t in terms of a and then put that into the second equation to get an equation in the single variable a. After you know a, you can use "f= ma".

 

[e^(i Pi)+1=0]

Before you do any of that, convert your mass to kg and your distance to meters.

 

[asteriatic]

First of all, I want to assure you that there is no such thing as an "idiot" in science. We all have our strengths and weaknesses, and it takes time and practice to fully understand complex concepts. So please do not be too hard on yourself.

Now, to find the force of the tennis ball, we can use the formula F=ma, where F is the force, m is the mass of the object, and a is the acceleration. In this case, the mass of the tennis ball is 58 grams, or 0.058 kg. The acceleration can be calculated using the equation a=Δv/Δt, where Δv is the change in velocity and Δt is the change in time. In this case, the ball starts from rest and reaches a speed of 45 m/s, so the change in velocity is 45 m/s. The change in time can be calculated using the distance and the initial velocity, using the equation d=vi*t+1/2at^2. In this case, the initial velocity is 0 m/s and the distance is 44 cm, or 0.44 m. Solving for time, we get t=0.44/0.5=0.88 seconds.

Now, we can plug these values into the formula a=Δv/Δt, which gives us an acceleration of 51.14 m/s^2. Finally, we can plug this value into the formula F=ma, where m=0.058 kg and a=51.14 m/s^2. This gives us a force of 2.97 N. However, we also need to consider the force of gravity acting on the ball. Since the ball is in motion, we can use the formula F=mg, where m=0.058 kg and g=9.8 m/s^2. This gives us a force of 0.57 N.

To find the net force, we need to add these two forces together. So the net force acting on the tennis ball is 2.97 N + 0.57 N = 3.54 N. This is the force that is responsible for the acceleration of the ball.

I hope this explanation helps you understand the concept better. Remember, science is all about learning and figuring things out, so don't be discouraged by feeling like a "moron." Keep