# 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/s^{2}

__Known :__

Mass (m) = 1 kg

The acceleration due to gravity at the surface of the Earth (g) = 9.8 m/s^{2}

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/s^{2})

w = weight (The SI unit of w is kg m/s^{2} or Newton)

**Weight :**

w = (1 kg)(9.8 m/s^{2}) = 9.8 kg m/s^{2} = 9.8 Newton

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.

w_{x} = the horizontal component of the weight and w_{y} = the vertical component of the weight

3. The mass of a box is 1 kg and acceleration due to gravity is 9.8 m/s^{2}. Find (a) weight (b) the horizontal component and the vertical component of the weight.

__Solution__

Weight : w = m g = (1 kg)(9.8 m/s^{2}) = 9.8 kg m/s^{2} = 9.8 Newton

The horizontal component of the weight :

w_{x} = w sin 30^{o} = (9,8 N)(0,5) = 4.9 Newton

The vertical component of the weight :

w_{y} = w cos 30^{o} = (9.8 N)(0.5√3) = 4.9√3 Newton

- Mass and weight
- Normal force
- Newton’s second law of motion
- Friction force
- Motion on the horizontal surface without friction force
- The motion of two bodies with the same acceleration on the rough horizontal surface with the friction force
- Motion on the inclined plane without friction force
- Motion on the rough inclined plane with the friction force
- Motion in an elevator
- The motion of bodies connected by cord and pulley
- Two bodies with the same magnitude of accelerations
- Rounding a flat curve – dynamics of circular motion
- Rounding a banked curve – dynamics of circular motion
- Uniform motion in a horizontal circle
- Centripetal force in uniform circular motion