How Does Vector Addition Determine Acceleration on a Frictionless Surface?

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Homework Help Overview

The problem involves analyzing the acceleration of a chopping block on a frictionless surface under the influence of two horizontal forces, with specific values given for each force in unit-vector notation. The context is rooted in the principles of vector addition and Newton's second law of motion.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of vector addition to determine the resultant force acting on the block. Questions arise regarding the role of mass in the equation F=ma and how to incorporate the resultant force into this equation.

Discussion Status

There is ongoing exploration of how to apply the vector addition of forces to find the resultant force and subsequently use it to determine acceleration. Some participants have provided guidance on rearranging the equation F=ma to isolate acceleration, but there is no explicit consensus on the final approach or calculations.

Contextual Notes

Participants are working within the constraints of the problem statement, which specifies different scenarios for the second force. There is an emphasis on understanding the implications of a resultant force of zero in the context of acceleration.

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Homework Statement



Two horizontal forces act on a 3.5 kg chopping block that can slide over a frictionless kitchen counter, which lies in an xy plane. One force is F1 = (3.1 N) + (7.8 N). Find the acceleration of the chopping block in unit-vector notation when the other force is (a) F2 = (-3.1 N) + (-7.8 N), (b) F2 = (-3.1 N) + (7.8 N), and (c) F2 = (3.1 N) + (-7.8 N).

Homework Equations



F=ma?

The Attempt at a Solution



I feel like I want to add vectors but I do not know where the mass comes into play other than in the equation F=ma
 
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Go with your feeling!

Use vector addition to get a single force on the board then use F = ma (more correctly the vector equation F = ma)
 
So the resulting force for a would be 3.1-3.1 which is 0 and then 7.8-7.8 which is 0. so? the resultant force is 0i+0j. But how would i use this in the F=ma formula
 
TS656577 said:
So the resulting force for a would be 3.1-3.1 which is 0 and then 7.8-7.8 which is 0. so? the resultant force is 0i+0j. But how would i use this in the F=ma formula
Rearrange as
a = F / m
then substitute your resultant force.
 
TS656577 said:
So the resulting force for a would be 3.1-3.1 which is 0 and then 7.8-7.8 which is 0. so? the resultant force is 0i+0j. But how would i use this in the F=ma formula

F = ma = mai + maj = 0i + 0j
 

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