In physics class, Carrie learns that a force, [tex]$F$[/tex], is equal to the mass of an object, [tex]$m$[/tex], times its acceleration, [tex]$a$[/tex]. She writes the equation [tex]$F=m a$[/tex].
Using this formula, what is the acceleration of an object with [tex]$F=7.92$[/tex] newtons and [tex]$m=3.6$[/tex] kilograms? Express your answer to the nearest tenth.
Note: The unit for Force (the Newton) is measured in [tex]$\frac{k g / m}{s^2}$[/tex].
A. [tex]$0.5 \frac{m}{s^2}$[/tex]
B. [tex]$1.8 \frac{m}{5^2}$[/tex]
C. [tex]$2.2 \frac{m}{ s ^2}$[/tex]
D. [tex]$4.9 \frac{m}{5^2}$[/tex]
Answer (2)
To find the acceleration of an object given a force of 7.92 newtons and a mass of 3.6 kilograms, we use the formula a = m F . By substituting in the values, we calculate the acceleration to be 2.2 s 2 m . Thus, the answer is option C: 2.2 s 2 m .
;
Use the formula F = ma .
Solve for acceleration: a = m F .
Substitute the given values: a = 3.6 7.92 .
Calculate the acceleration: a = 2.2 s 2 m .
Explanation
Understanding the Problem We are given the formula F = ma , where F is the force, m is the mass, and a is the acceleration. We are given F = 7.92 newtons and m = 3.6 kilograms. We need to find the acceleration a .
Isolating Acceleration To find the acceleration, we can rearrange the formula to solve for a : a = m F
Substituting Values Now, we substitute the given values into the formula: a = 3.6 7.92
Calculating Acceleration Calculating the value of a : a = 2.2
Final Answer Therefore, the acceleration of the object is 2.2 s 2 m .
Examples
Understanding the relationship between force, mass, and acceleration is crucial in many real-world scenarios. For example, when designing a car, engineers need to calculate the force required to accelerate the car to a certain speed. If the car's mass is known, they can use the formula F = ma to determine the necessary force. Similarly, in sports, understanding this relationship helps athletes optimize their performance. For instance, a baseball player can increase the acceleration of the ball by applying more force during a swing. The greater the force applied to the ball (with a constant mass), the greater the acceleration, and thus the faster the ball travels.
