6.1 Mass, Weight and Gravity

Chapter 6 Objectives  Calculate the weight of an object using the strength of gravity (g) and mass.  Describe the difference between mass and weight.  Describe at least three processes that cause friction.  Calculate the force of friction on an object when given the coefficient of friction and normal force.  Calculate the acceleration of an object including the effect of friction.  Draw a free-body diagram and solve one-dimensional equilibrium force problems.  Calculate the force or deformation of a spring when given the spring constant and either of the other two variables.

Chapter 6 Vocabulary  ball bearings  coefficient of friction  coefficient of static friction  compressed  deformation  dimensions  lubricant  normal force  prototype  restoring force  rolling friction  sliding friction  engineering  engineering cycle  extended  free-body diagram  g forces  Hooke’s law  spring  spring constant  static friction  subscript  viscous friction  weightless

Inv 6.1 Mass versus Weight Investigation Key Question: How are mass and weight related on Earth?

6.1 Mass, Weight, and Gravity  Mass is a measure of matter.  Mass is constant.  Weight is a force.  Weight is not constant.

6.1 Mass, Weight, and Gravity  The weight of an object depends on the strength of gravity wherever the object is.  The mass always stays the same.

6.1 Calculating weight with mass and gravity  The weight of an object depends on its mass and the strength of gravity.  The formula gives the weight (F w ) in terms of the mass of an object, m, and the strength of gravity, g.

6.1 Two meanings for “g”  The symbol g stands for the acceleration of gravity in free fall, which is 9.8 m/s 2.  Another meaning for g is the strength of gravity, which is 9.8 N/kg.  Sometimes it is more natural to discuss gravity in N/kg instead of m/s 2 because objects may not be in motion but they still have weight.  The two meanings for g are equivalent since a force of 9.8 N acting on a mass of 1 kg produces an acceleration of 9.8 m/s 2.

6.1 Gravity, acceleration and weightlessness  An object is weightless when it experiences no net force from gravity.  If an elevator is accelerating downward at 9.8 m/sec 2, the scale in the elevator shows no force because it is falling away from your feet at the same rate you are falling.

6.1 Gravity, acceleration and weightlessness  Airplane pilots and race car drivers often describe forces they feel from acceleration as g forces.  These g forces are not really forces at all, but are created by inertia.  Remember, inertia is resistance to being accelerated.

6.1 Using weight in physics problems  Like other forces, weight is measured in newtons or pounds.  Very often, weight problems involve equilibrium where forces are balanced.  The other common type of weight problem involves other planets, or high altitudes, where the strength of gravity (g) is not the same as on Earth’s surface.

1.You are asked to find force. 2.You are given a mass of 10 kilograms. 3.The force of the weight is Fw = mg and g = 9.8 N/kg. 4.The word “supported” means the ball is hanging motionless at the end of the rope. That means the tension force in the rope is equal and opposite to the weight of the ball.  Fw = (10 kg) × (9.8 N/kg) = 98 N.  The tension force in the rope is 98 newtons. Calculating force required to hold up an object  A 10-kilogram ball is supported at the end of a rope. How much force (tension) is in the rope?

1.You are asked for the weight. 2.You are given the weight on Earth and the strength of gravity on Jupiter. 3.Use Fw = mg. 4.First, find the person’s mass from weight on Earth:  m = (490 N) ÷ (9.8 N/kg) = 50 kg.  Next, find the weight on Jupiter:  Fw = (50 kg) × (23 N/kg) = 1,150 N (259 lbs) Calculating weight on Jupiter How much would a person who weighs 490 N (110 lbs) on Earth weigh on Jupiter? Since Jupiter may not have a surface, on means at the top of the atmosphere. The value of g at the top of Jupiter’s atmosphere is 23 N/kg.