Question

A rope is used to pull a 1.39-kg bucket of water out of a deep well. In m/s^2, what is the acceleration of the bucket when the tension in the rope is 20.2 N?Answer: ________ m/s^2

Answer 1

4.73 m/s²

Step-by-step explanation:

The free body diagram for the bucket is

Then, the net force is equal to

Fnet = T - mg = ma

Where T is the tension of the rope, m is the mass, g is the gravity, and a is the acceleration. Solving for a, we get:

`\begin{gathered} T-mg=ma \\ \\ a=(T-mg)/(m) \end{gathered}`

Replacing T = 20.2 N, m = 1.39 kg, and g = 9.8 m/s², we get

`\begin{gathered} a=\frac{20.2\text{ N - \lparen1.39 kg\rparen\lparen9.8 m/s}^2)}{1.39\text{ kg}} \\ \\ a=\frac{20.2\text{ N - 13.622 N}}{1.39\text{ kg}} \\ \\ a=\frac{6.578\text{ N}}{1.39\text{ kg}} \\ \\ a=4.73\text{ m/s}^2 \end{gathered}`

Therefore, the acceleration is 4.73 m/s²