A ball weighing 1.78 N is shot through a launcher,achieving a speed (from rest) of 41 m/s in 0.28s. What is the mass of the ball.

To find the mass of the ball, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration.

Here, we are given the weight of the ball, which is the force acting on the ball. The weight of the ball is given as 1.78 N.

So, we can write the equation as:

Force = mass × acceleration

In this case, the force acting on the ball is its weight, given as 1.78 N. The acceleration can be calculated using the formula:

acceleration = (final velocity - initial velocity) / time

The final velocity is given as 41 m/s, the initial velocity is 0 m/s (since it starts from rest), and the time is given as 0.28s.

Now we can substitute the given values into the equation and solve for acceleration:

acceleration = (41 m/s - 0 m/s) / 0.28s
acceleration = 41 m/s / 0.28s
acceleration ≈ 146.43 m/s^2

Now, we can substitute the values of force and acceleration into the equation to find the mass of the ball:

1.78 N = mass × 146.43 m/s^2

To solve for mass, we divide both sides of the equation by 146.43 m/s^2:

mass = 1.78 N / 146.43 m/s^2
mass ≈ 0.0122 kg

Therefore, the mass of the ball is approximately 0.0122 kg.