Question

An object of mass 6.3 kg is suspended on a string from the ceiling of a moving elevator. Given 9.8 m/s^2 for gravity and the string tension 30.24 N, find the elevator’s acceleration a. In your answer, take upward acceleration to be positive and downward acceleration to be negative. Answer in units of m/s^2 .

Answer 1

Answer:

The elevator's acceleration is -5 (j) m/s²

Explanation:

In order to obtain the acceleation, you have to apply Newton's Second Law, which is:

∑F =mA

Where F are all the acting forces, m is the mass and A is the acceleration.

Notice that the acceleration of the elevator is the acceleation of the object, because they can be seen as a system.

The acting forces are: The tension (T) pointing upward (because the string is suspended from the ceiling) and the weight (W) pointing downward because the weight is produced by the gravity force which points to the ground.

Applying Newton's Second Law:

y-axis: T-W=mA

T-mg=mA

Solving for A:

$A=\frac{T-mg}{m}$

$A=\frac{30.24-(6.3)(9.8)}{6.3}= -5$ m/s²

Therefore, the acceleration vector is: -5 (j) m/s² (where j is the unit vector in the y direction)