a 4.1 kg bucket of water is raised from a well by a rope.
The acceleration of gravity is 9.8 m/s^2
If the upward acceleration of the bucket is 2.7 m/s^2 find the force exerted by the rope on the bucket. Use g=9.8 m/s^2
force=mass(g+a)
To find the force exerted by the rope on the bucket, we can use Newton's second law of motion, which states that force equals mass times acceleration (F = m * a).
Given:
Mass of the bucket (m) = 4.1 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Upward acceleration of the bucket (a) = 2.7 m/s^2
First, we need to determine the net force acting on the bucket. The net force is the force exerted by the rope minus the force due to gravity. We can calculate the force due to gravity using the formula:
Force due to gravity = mass * acceleration due to gravity
= m * g
Substituting the values we have:
Force due to gravity = 4.1 kg * 9.8 m/s^2
= 40.18 N
Next, we can calculate the net force by subtracting the force due to gravity from the force exerted by the rope. Let's call the force exerted by the rope F:
Net force = F - Force due to gravity
We know that the net force is equal to mass times acceleration (F_net = m * a). Rearranging this equation, we get:
F = F_net + Force due to gravity
Substituting the given values:
F = (4.1 kg * 2.7 m/s^2) + 40.18 N
= 11.07 N + 40.18 N
= 51.25 N
Therefore, the force exerted by the rope on the bucket is 51.25 Newtons.