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Word Problems (Second Law) Part 2

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Word Problem

Which would require a greater force –– accelerating a 5 kg mass at 8 m/s2 or a 6 kg mass at 7 m/s2?

Solution

We already know that Newton’s second law of motion states that the force applied on an object

is the product of the object’s mass and its acceleration.

For the first case, let the mass = m1 and acceleration = a1. For the second case, let the mass = m2 and acceleration = a2.

Let’s calculate the force for both the cases.

First case Second case
Mass m1 = 5 kg m2 = 6 kg
Acceleration a1 = 8 m/s2 a2 = 7 m/s2
Force F1 = m1 X a1

= 5 kg X 8 m/s2

= 40 N

 F2 = m2 X a2

= 6 kg X 7 m/s2

= 42 N

Since the magnitude of force in the second case is greater than the first case, accelerating a 6 kg mass at 7 m/s2 will require greater force than accelerating a 5 kg mass at 8 m/s2.

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