Question

Bucket Lift. You are using a rope to lift a 2-kg bucket from the ground to a second-floor window. If the upward tension force on the bucket is 25 N, determine the acceleration of the bucket. (Hint: Don’t forget the downward force of gravity on the bucket, i.e. its weight)

Answer 1

Answer:

2.7 m/s²

Explanation:

$\underline{\bigstar\:\textsf{Given:}}$

• Mass of bucket (m) = 2 kg
• Upward tension (T) = 25 N

$\underline{\bigstar\:\textsf{To\:find:}}$

• Acceleration of the bucket (a) = ?

$\underline{\bigstar\:\textsf{Solution:}}$

Let's analyze the situation !

You are lifting a bucket of mass (m) 2 kg using a rope from wthe ground to a second-floor window, the upward tension (T) on the bucket is 25 N and we have to determine the acceleration (a) of the bucket.

Let's find now !

We remember that incases of lifting any object the tension is $\blue{\sf{T\:=\:mg\:+ma.}}$

(Let's put the given values)

$\longrightarrow$ 25 = 2 × 9.8 + 2 × a

$\longrightarrow$ 25 = 19.6 + 2 + a

$\longrightarrow$ 25 - 19.6 = 2 × a

$\longrightarrow$ 5.4 = 2 × a

$\longrightarrow\:\dfrac{5.4}{2}\:=\:a$

$\implies$ 2.7 m/s² = a

${\large{\boxed{\sf{\therefore \: Acceleration(a)\:=\:2.7\:m/s^2}}}}$

____________________________

Answer 2

GIVEN :

• Mass of a bucket = 2 kg
• Upward tension force on the bucket = 25 N
• We are considering the gravitation value (g) = 9.8 m/s².

TO FIND :

• Acceleration of the bucket = ?

FORMULAS USED :

• T = mg + ma

SOLUTION :

The tension of lifting an object : T = mg + ma.

Put the given values in the above formula.

To find the acceleration = ?

$\implies \bf 25 \: = \: 2 \: \times \: 9.8 \: + \: 2 \: \times \: a$

$\implies \bf 25 \: = \: 19.6 \: + \: 2 \: + \: a$

$\implies \bf 25 \: - \: 19.6 \: = \: 2 \: \times \: a$

$\implies \bf 5.4 \: = \: 2 \: \times \: a$

$\implies \bf \dfrac {5.4}{2} \: = \: a$

$\implies \bf a \: = \: 2.7 \: m/s^{2}$

$\therefore \Large \red {\boxed {\bf a \: = \: 2.7 \: m/s^{2}}}$

$\therefore$ The acceleration of the bucket is 2.7 m/s².