A ball has a mass of 140 g. What is the force needed to accelerate the ball at [tex]$25 m / s ^2$[/tex]? (Formula: [tex]$F= ma$[/tex])
Answer (1)
Convert the mass from grams to kilograms: m = 1000 140 = 0.14 k g .
Use the formula F = ma to calculate the force.
Substitute the values: F = 0.14 k g × 25 m / s 2 .
Calculate the force: 3.5 N .
Explanation
Understanding the Problem We are given the mass of a ball, m = 140 g , and its acceleration, a = 25 m / s 2 . We need to find the force required to accelerate the ball using the formula F = ma .
Converting Units First, we need to convert the mass from grams to kilograms since the standard unit for mass in the formula F = ma is kilograms. We know that 1 kg = 1000 g, so we can convert the mass as follows: m ( k g ) = 1000 m ( g ) = 1000 140 = 0.14 k g
Calculating the Force Now that we have the mass in kilograms, we can use the formula F = ma to calculate the force: F = ma = ( 0.14 k g ) × ( 25 m / s 2 ) = 3.5 N
Final Answer Therefore, the force needed to accelerate the ball at 25 m / s 2 is 3.5 N.
Examples
Imagine you're pushing a shopping cart. The heavier the cart (mass) and the faster you want it to speed up (acceleration), the more force you need to apply. This problem illustrates the fundamental relationship between force, mass, and acceleration, which is crucial in understanding how objects move in our everyday lives. For example, if you want to calculate how much force your car engine needs to produce to accelerate your car to a certain speed, you would use the same formula.
