A bowling ball weighing 40.0 N initially moves at a speed of 4.90 m/s. How long must a force of 54.0 N be applied to the ball to stop it?
To find the time required to stop the bowling ball, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
Fnet = ma
In this case, the net force is the force applied to the ball to stop it, which is 54.0 N. The mass of the ball is not given directly, but we can use the weight of the ball to find its mass:
Weight = mass x gravitational acceleration
Since weight is given as 40.0 N and the acceleration due to gravity is approximately 9.8 m/s^2, we can rearrange the equation to solve for mass:
mass = weight / gravitational acceleration
mass = 40.0 N / 9.8 m/s^2
mass ≈ 4.08 kg
Now that we have the mass of the ball, we can calculate the acceleration using the equation Fnet = ma:
54.0 N = 4.08 kg x a
a ≈ 13.24 m/s^2
The negative sign indicates that the acceleration is opposite in direction to the initial velocity of the ball, as it is being slowed down.
Now, to find the time needed to stop the ball, we can use the equation of motion:
v = u + at
Where:
- v is the final velocity (0 m/s, since the ball comes to a stop)
- u is the initial velocity (4.90 m/s)
- a is the acceleration (-13.24 m/s^2)
Substituting the values into the equation:
0 = 4.90 m/s + (-13.24 m/s^2) x t
Simplifying the equation:
-4.90 m/s = -13.24 m/s^2 x t
Dividing both sides of the equation by -13.24 m/s^2:
t = (-4.90 m/s) / (-13.24 m/s^2)
t ≈ 0.37 s
Therefore, a force of 54.0 N needs to be applied to the ball for approximately 0.37 seconds to stop it.