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 how to determine the acceleration of a 5-kg object when a 20-N force is applied to it on a frictionless surface. We can use Newton's second law of motion, which states that the acceleration (a) is equal to the net force (F) divided by the mass (m) of the object (a = F/m).
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 given values
Recognize the information provided in the problem:
- Mass of the object, $m = 5 \text{ kg}$
- Applied force, $F = 20 \text{ N}$
- Use Newton's Second Law
According to Newton's second law of motion, the formula for acceleration is given by: $$ a = \frac{F}{m} $$
Substituting the given values into the equation: $$ a = \frac{20 \text{ N}}{5 \text{ kg}} $$
- Calculate the acceleration
Perform the calculation to find the acceleration: $$ a = 4 \text{ m/s}^2 $$
The acceleration of the object is $4 \text{ m/s}^2$.
More Information
The acceleration found shows how quickly the object is speeding up when subjected to the applied force. This concept illustrates the fundamental principle of dynamics, where greater forces lead to greater accelerations, assuming a constant mass.
Tips
- Confusing mass with weight: Remember that mass is a measure of how much matter is in an object (in kg), while weight is the force due to gravity (in N).
- Forgetting to divide the applied force by mass: Ensure that the correct formula $a = \frac{F}{m}$ is used.
