# Mass and weight – problems and solutions

Solved problems in Newton’s laws of motion – Mass, and weight

1. The weight of a 1 kg mass at the surface of the Earth is… g = 9.8 m/s2

Known :

Mass (m) = 1 kg

The acceleration due to gravity at the surface of the Earth (g) = 9.8 m/s2

Wanted: weight (w)

Solution :

w = m g

m = mass (The SI unit of mass is the kilogram, kg)

g = acceleration due to gravity (The SI unit of g is m/s2)

w = weight (The SI unit of w is kg m/s2 or Newton)

Weight :

w = (1 kg)(9.8 m/s2) = 9.8 kg m/s2 = 9.8 Newton

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2.

(a) Draw the force of gravity (weight) that act on the object when the object is at rest on a table, as shown in figure (a).

(b) Draw the force of gravity (weight) and it’s components that act on an object sliding down an inclined plane, as shown in figure (b) Solution The direction of the weight is downward toward the center of the Earth.

wx = the horizontal component of the weight and wy = the vertical component of the weight

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3. The mass of a box is 1 kg and acceleration due to gravity is 9.8 m/s2. Find (a) weight (b) the horizontal component and the vertical component of the weight. Solution

Weight : w = m g = (1 kg)(9.8 m/s2) = 9.8 kg m/s2 = 9.8 Newton

The horizontal component of the weight :

wx = w sin 30o = (9,8 N)(0,5) = 4.9 Newton

The vertical component of the weight :

wy = w cos 30o = (9.8 N)(0.5√3) = 4.9√3 Newton

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