What is the mass of a crate if a force of 200 N causes it to accelerate at [tex]$8 m / s ^2$[/tex]? (Formula: [tex]$F=m a$[/tex])
Answer (1)
Use the formula F = ma to relate force, mass, and acceleration.
Rearrange the formula to solve for mass: m = a F .
Substitute the given values: m = 8 200 .
Calculate the mass: 25 k g .
Explanation
Understanding the Problem We are given the force applied to a crate and its resulting acceleration, and we are asked to find the mass of the crate. We know the formula that relates force, mass, and acceleration: F = ma , where F is the force, m is the mass, and a is the acceleration.
Solving for Mass We need to rearrange the formula F = ma to solve for the mass m . Dividing both sides of the equation by a , we get: m = a F
Substituting Values Now, we substitute the given values into the formula. We have F = 200 N and a = 8 m / s 2 . Therefore, m = 8 m / s 2 200 N = 25 k g
Final Answer The mass of the crate is 25 kg.
Examples
Imagine you're pushing a shopping cart. The heavier the cart (mass), the harder it is to accelerate. If you apply a force of 200 N and the cart accelerates at 8 m / s 2 , its mass is 25 kg. This concept is crucial in physics and engineering for designing vehicles, calculating the force needed to move objects, and understanding motion.
