Question

A clarinetist, setting out for a performance, grabs his 3.130 kg 3.130 kg clarinet case (including the clarinet) from the top of the piano and carries it through the air with an upward force of 38.38 N. 38.38 N. Find the case's vertical acceleration. Indicate an upward acceleration as positive and a downward one as negative.

Answer 1

`+2.46 m/s^2`

Step-by-step explanation:

There are two forces acting on the clarinet case:

- The upward force, F, of magnitude

F = 38.38 N

- The force of gravity, downward, of magnitude

`W=mg`

where

m = 3.130 kg is the mass of the case

`g=9.8 m/s^2` is the acceleration due to graviry

According to Newton's second law of motion, the net force is equal to the product between mass and acceleration of the case:

`F-W=ma`

where a is the acceleration.

Solving for a, we find:

`a=(F-mg)/(m)=(38.38-(3.130)(9.8))/(3.130)=2.46 m/s^2`

And the direction is upward, since the result is positive (same sign as the upward force).