A horizontal force is applied to a 2-kg ball on a smooth table. The ball's speed is 6 m/s when it has gone 3 m. The magnitude of the force is
To find the magnitude of the force applied to the ball, we can use Newton's second law, which states that force is equal to mass multiplied by acceleration.
In this case, the mass of the ball is given as 2 kg. We need to find the acceleration of the ball to calculate the force.
We know that the speed of the ball is changing because it is moving in a straight line. Therefore, the ball is experiencing acceleration.
To find the acceleration of the ball, we can use the equation:
v^2 = u^2 + 2as
where:
v = final velocity (6 m/s)
u = initial velocity (0 m/s, since the ball starts from rest)
a = acceleration
s = displacement (3 m)
Plugging in the values, we get:
6^2 = 0^2 + 2a(3)
Simplifying, we have:
36 = 6a
Dividing both sides by 6, we find that the acceleration is:
a = 6 m/s^2
Now, we can use Newton's second law to calculate the force:
F = ma
Plugging in the values, we have:
F = 2 kg * 6 m/s^2
Calculating, we find that the magnitude of the force applied to the ball is:
F = 12 N