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A 44 kg child steps onto a scale and the scale reads 431 N. What is the magnitude of the normal force acting on the child?

A) 431 N
B) 44 N
C) 860 N
D) 215 N
E) 645 N

Answer :

Final answer:

Given the provided force reading from the scale and the established equivalence of 1 N = 1 kg.m/s², the weight that corresponds to the force exerted by the child is found to be 431 N. As long as the child is not accelerating, this is equal to the normal force exerted on the child.

Explanation:

The magnitude of the normal force acting on the child can be determined by translating the value of the force from Newtons (N) back to weigh (kg). We're given that the scale reads 431N. Given that 1 N = 1 kg.m/s², the weight that corresponds to this force can be calculated using the formula for force: F = m * a, where F is the force (data from the scale), m is the mass (the mass of the child), and a is the acceleration (gravity on Earth which equals approximately 9.8 m/s²).

Transforming the equation to find m (mass), we get m = F / a. As long as the child is not accelerating (which means they are at rest or moving at a constant velocity), the force exerted on the scale, which is the weight of the child, is equal to the normal force exerted by the scale on the child (according to Newton's Third Law of Motion). Hence, the normal force in this case is indeed 431 N, which corresponds to option (A).

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