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Chapter 1: Problem 40

An object has a mass of \(8 \mathrm{~kg}\). Determine (a) its weight at a location where the acceleration of gravity is \(g=9.7 \mathrm{~m} / \mathrm{s}^{2}\), (b) the magnitude of the net force, in \(\mathrm{N}\), required to accelerate the object at \(7 \mathrm{~m} / \mathrm{s}^{2}\).

Short Answer

Expert verified
The weight of the object at a location where \( g = 9.7 m/s^2 \) is \( 77.6 N \) and the magnitude of the net force required to accelerate the object at \( 7 m/s^2 \) is \( 56 N \).

Step by step solution

01

Calculate the weight of the object

The weight of an object can be found by multiplying its mass by the acceleration due to gravity at its location. The acceleration due to gravity \( g \) is given as \( 9.7 m/s^2 \). The mass of the object is given as \( 8 kg \). Therefore, the weight can be calculated using the formula \( Weight = mass \times gravity \). Hence, the weight is \( Weight = 8 kg \times 9.7 m/s^2 \).
02

Calculate the net force required to accelerate the object

The net force required to accelerate an object can be found by multiplying its mass by the required acceleration. The acceleration given in the problem is \( 7 m/s^2 \) and the mass of the object is \( 8 kg \). Therefore, the net force can be calculated using the formula \( Force = mass \times acceleration \). Hence, the net force is \( Force = 8 kg \times 7 m/s^2 \).

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