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]$F= ma$[/tex])
Answer (2)
We are given the force F = 200 N and acceleration a = 8 m / s 2 .
We use the formula F = ma to relate force, mass, and acceleration.
We rearrange the formula to solve for mass: m = a F .
We substitute the given values to find the mass: m = 8 200 = 25 k g . The final answer is 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 these three quantities is F = ma , where F is the force, m is the mass, and a is the acceleration.
Rearranging the Formula 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 the 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
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 achieve a certain acceleration, which directly impacts the engine's power and the car's overall performance. Similarly, in sports, knowing how much force an athlete can generate helps determine the mass of the equipment they can effectively use, such as the weight they can lift or the ball they can throw. These calculations ensure safety, efficiency, and optimal performance in various applications.
To find the mass of the crate, we use the formula F = ma and rearrange it to m = a F . Substituting the values, we find that the mass is 25 k g .
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