Final answer:
The acceleration of the piano Amirah and Dana are moving is calculated using Newton's second law. After considering the forces they exert and the friction force, the net force is found to be 270 N. Dividing this by the piano's mass, which is approximately 18.37 kg, the piano's acceleration is determined to be 14.7 m/s².
Step-by-step explanation:
To calculate the acceleration of the piano, we need to apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass (F = ma). In this case, we will find the net force by adding the force exerted by Amirah and Dana and then subtracting the friction force.
First, let's sum up the forces parallel to the motion:
- Force by Amirah: 300 N (pushing)
- Force by Dana: 200 N (pulling)
- Friction force: -230 N (acting in the opposite direction to motion)
Next, we calculate the net force:
Net force = Amirah's force + Dana's force - Friction
Net force = 300 N + 200 N - 230 N = 270 N
Now, let's find the mass in kilograms. Since force equals mass times acceleration due to gravity (F = mg, with g approximately equal to 9.8 m/s²), we can calculate mass as:
Mass = Force / Acceleration due to gravity
Mass = 180 N / 9.8 m/s² ≈ 18.37 kg
Finally, we use Newton's second law to find the acceleration:
Acceleration (a) = Net force / Mass
Acceleration = 270 N / 18.37 kg ≈ 14.7 m/s²
Since the question asks for the answer to the nearest tenth, the acceleration of the piano is 14.7 m/s².