A 20-N force acts on a 5-kg object at rest. How fast will the object accelerate on a frictionless surface?
Understand the Problem
The question is asking for the acceleration of a 5-kg object when a 20-N force is applied to it while the object is on a frictionless surface. We will use Newton's second law of motion, F = ma, to find the acceleration.
Answer
The acceleration is $4 \, \text{m/s}^2$.
Answer for screen readers
The acceleration of the object is $4 , \text{m/s}^2$.
Steps to Solve
- Identify the variables First, let's define the variables we have in the problem:
- Mass of the object, ( m = 5 , \text{kg} )
- Applied force, ( F = 20 , \text{N} )
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Use Newton's second law of motion We apply Newton's second law, which states that the force acting on an object is equal to its mass times its acceleration: $$ F = ma $$
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Rearrange the equation To find the acceleration ( a ), we can rearrange the equation: $$ a = \frac{F}{m} $$
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Plug in the values Now, substitute the values we have: $$ a = \frac{20 , \text{N}}{5 , \text{kg}} $$
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Calculate the acceleration Finally, perform the division to find the acceleration: $$ a = 4 , \text{m/s}^2 $$
The acceleration of the object is $4 , \text{m/s}^2$.
More Information
This acceleration shows how quickly the 5-kg object will increase its speed when subjected to a 20-N force. Since there is no friction, all of the applied force contributes to the acceleration.
Tips
- Misunderstanding Newton's second law and mixing up the relationship between force, mass, and acceleration. Always remember that force equals mass times acceleration.
- Not converting units if necessary. Make sure all units are compatible (e.g., using kg for mass, N for force).
