A rope is used to pull a 2.89-kg bucket of water out of a deep well. The tension in the rope is 30.2 N. If starting from rest, what speed will the bucket have after experiencing this force for 2.16 seconds? Select the correct value and the correct units.
To find the speed of the bucket after experiencing the tension force for 2.16 seconds, we can use Newton's second law of motion.
Newton's second law states that the net force acting on an object is equal to the product of its mass and acceleration:
F = ma
Where:
F is the net force (tension in the rope)
m is the mass of the object (2.89 kg)
a is the acceleration of the object
We can rearrange the equation to solve for acceleration:
a = F/m
Now we can calculate the acceleration:
a = 30.2 N / 2.89 kg = 10.46 m/s²
Next, we can use one of the kinematic equations to determine the final velocity (v) of the bucket. Since the initial velocity is zero (starting from rest), we can use the following equation:
v = u + at
Where:
v is the final velocity
u is the initial velocity (zero in this case)
a is the acceleration (10.46 m/s²)
t is the time (2.16 seconds)
Now we can calculate the final velocity of the bucket:
v = 0 + 10.46 m/s² x 2.16 s = 22.6 m/s
Therefore, the correct value for the speed of the bucket after experiencing the tension force for 2.16 seconds is 22.6 m/s.