Which launch had the greatest acceleration of the tennis ball?
To solve this problem we must apply Newton's second law, which tells us that the sum of forces on a body is equal to the product of mass by acceleration and this force can be calculated by means of the following equation.
F = m*a
where:
F = force [N] (units of Newtons)
m = mass [kg]
a = acceleration [m/s²]
The mass of the tennis ball will always be the same therefore it will never change.
Now clearing a:
a = F/m
If the mass of the ball remains the same:
a = 100/m ; a = 200/m; a = 300/m
We see that for a force of 300 [N], the acceleration exerted on the ball must be greater. Therefore with the force of 300 [N] the greatest acceleration is achieved.
Explanation:
Newton's Second Law:
Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This law is represented by the equation F = m*a, where F is the force applied to the object, m is the mass of the object, and a is the acceleration produced.
Application to Tennis Ball Launch:
In the scenario provided, Tessa uses different forces (100 N, 200 N, 300 N) to launch the tennis ball. Since the mass of the tennis ball remains constant, we can calculate the acceleration produced by each force using the formula a = F/m.
- For the first launch with a force of 100 N: a = 100/m
- For the second launch with a force of 200 N: a = 200/m
- For the third launch with a force of 300 N: a = 300/m
Analysis:
As the force applied increases, the acceleration of the tennis ball also increases. This is because acceleration is directly proportional to force when mass is constant. Therefore, the launch with 300 N of force resulted in the greatest acceleration of the tennis ball.
In conclusion, the launch with 300 N of force had the greatest acceleration of the tennis ball due to the direct relationship between force and acceleration described by Newton's second law of motion.