Calculating Forces and Acceleration of a Grand Piano

In summary, in this conversation, the question is asked to determine the net force and acceleration of a grand piano being moved by three movers applying forces in specific directions. The attempted solution calculates a net force of 482.38N going down and 276.9N going left, but the answer sheet gives a net force of 106N. It is then clarified that the direction of motion is in the direction of the acceleration and that the direction of the friction force must be accounted for in the calculation of the resultant force.
  • #1
nesan
75
0

Homework Statement



Three movers are applying forces F1 = 100 N [W20°N], F2 = 200 N [E40°S], and F3 = 300 N on a 300-kg grand piano. If μK for the piano is 0.10, determine
a) the net force acting on the piano
b) the acceleration of the piano

The Attempt at a Solution



34rap83.png


I got an answer of 395 N going down and 276.9 going left.

Fnet = 482.38N

But the answer sheet says 106N

:(

Help please.
 
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  • #2
nesan said:

Homework Statement



Three movers are applying forces F1 = 100 N [W20°N], F2 = 200 N [E40°S], and F3 = 300 N on a 300-kg grand piano. If μK for the piano is 0.10, determine
a) the net force acting on the piano
b) the acceleration of the piano

The Attempt at a Solution



34rap83.png


I got an answer of 395 N going down and 276.9 going left. (Actually is East, not left.)

Fnet = 482.38N

But the answer sheet says 106N

:(

Help please.

How in the world do you get 276.9 N going left?
 
  • #3
SammyS said:
How in the world do you get 276.9 N going left?

I subtracted the amount of force going right from the friction. Is that wrong?
 
  • #4
nesan said:
I subtracted the amount of force going right from the friction. Is that wrong?

In which direction does the friction force act?
 
  • #5
nesan said:
I subtracted the amount of force going right from the friction. Is that wrong?
That's wrong.

These are compass directions.

The positive y direction is North, not up, etc.

Gravity acts in the direction into the page. The normal force is out of the page.


Find the resultant force for the three given forces. Assuming that the direction of motion is in the direction of the acceleration, you can then account for the direction in which the friction force acts.
 

Related to Calculating Forces and Acceleration of a Grand Piano

1. How do you calculate the force needed to lift a grand piano?

To calculate the force needed to lift a grand piano, you would need to know the weight of the piano and the acceleration due to gravity. The formula for force, F = m * a, can then be used to calculate the force needed. Simply plug in the weight of the piano in kilograms for m, and the acceleration due to gravity (9.8 m/s^2) for a. This will give you the force needed to lift the piano in Newtons.

2. How do you calculate the acceleration of a grand piano?

To calculate the acceleration of a grand piano, you would need to know the force applied to the piano and its mass. The formula for acceleration, a = F/m, can then be used to calculate the acceleration. Simply plug in the force applied in Newtons for F, and the mass of the piano in kilograms for m. This will give you the acceleration of the piano in meters per second squared.

3. How does the shape and size of a grand piano affect its acceleration?

The shape and size of a grand piano can affect its acceleration in a few ways. A larger piano will have a greater mass, which will require more force to accelerate. The shape of the piano can also affect its aerodynamics, which can impact the amount of force needed to move it. Additionally, the shape and size of a grand piano can affect its center of mass, which can impact its stability and acceleration when being moved.

4. Can you calculate the force and acceleration of a grand piano while it is in motion?

Yes, it is possible to calculate the force and acceleration of a grand piano while it is in motion. However, this would require additional information such as the velocity and direction of the piano's movement. The formulas for force and acceleration would then need to be adjusted to take into account the piano's velocity and direction.

5. How can knowing the forces and acceleration of a grand piano be useful?

Knowing the forces and acceleration of a grand piano can be useful for a variety of reasons. It can help determine the amount of force needed to lift or move the piano, as well as the best angle and direction to apply the force. It can also be helpful for understanding the piano's stability and potential risks of tipping or falling. Additionally, this information can be useful for designing and constructing equipment used for moving pianos, such as dollies or cranes.

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