Application of Forces

Objective: To apply Newton’s Laws of motion to analyze accelerated motion as it applies to a vertically accelerated object and the apparent forces acting.

Forces Force of Gravity

Gravitational Force or Weight, F g = W Force due to the pull of the planet (Earth) on an object Force due to Gravity

F g = W = Weight = Force of Gravity Weight is different than mass !!!!!! Weight IS the gravitational force acting on the object.

Force due to Gravity  Mass is the amount of matter in an object.  Mass does not change regardless of where the object is located

Force due to Gravity Gravitational Force or Weight, F g or W. g = -9.8 m/s 2

 The slope of a weight vs. mass graph is the acceleration of gravity. W(N) mass (kg)

The elevator is an application of Newton’s 2 nd Law.

- a+ a

Elevator Problem An 800 N man stands on a scale in an elevator. What is the scale reading when (a) it is ascending a constant velocity of 3 m/s (b) descending at the same rate (c) ascending with acceleration of 0.8 m/s 2 (d) descending with acceleration of 0.8 m/s 2 ? Upward force of scale Downward force of weight

Force due to Gravity There are 3 cases to be considered. Case I: An object moving vertically with constant velocity.  F = ma F – F g = ma where a = 0 therefore F – F g = m(0) F – F g = 0 * F = F g *

Elevator Problem An 800 N man stands on a scale in an elevator. What is the scale reading when (a) it is ascending a constant velocity of 3 m/s? Upward force of scale Downward force of weight Net force = 0 Acceleration = 0 Scale reads normal weight In any unaccelerated system (constant velocity) the scale reading equals normal weight, therefore in parts (a) and (b) the scale reads 800 N

Force due to Gravity Case II: An object moving vertically upward and accelerating.  F = ma F – F g = ma therefore * F = F g + ma * The force F, is now larger than the force of gravity by the amount of ma.

Elevator Problem (cont’d) Upward force of scale (P) Downward force of weight Net force > 0 (up) Acceleration = + Scale reads > normal weight Force net = upward push of scale (+) + weight downward (-) Solve for Force of the scale: The scale reading is greater than the normal weight reading of 800 nts and upward acceleration occurs

Force due to Gravity Case III: An object moving vertically downward and accelerating.  F = ma F – F g = m(-a) therefore * F = F g - ma * The force F, is now smaller than the force of gravity by the amount of ma.

Upward force of scale (P) Downward force of weight Net force < 0 (down) Acceleration = - Scale reads < normal weight Force net = upward push of scale (+) + weight downward (-) Solve for the upward force on scale The scale reading is less than the normal weight reading of 800 N and downward acceleration occurs Elevator Problem (cont’d)

Scale Reading 100 lbs Scale Reading 125 lbs GOING UP Acceleration = + 8 ft/s 2 Scale Reading 75 lbs GOING DOWN Acceleration = - 8 ft/s 2 Net force = MA T + W = MA T = tension in elevator cable W = weight

Upward force of scale Downward force of weight Net force = 0 Acceleration = 0 Scale reads normal weight Upward force of scale Downward force of weight Net force = up Acceleration = + Scale reads > normal weight Upward force of scale Downward force of weight Net force = down Acceleration = - Scale reads < normal weight

Force due to Gravity A brother and sister while fishing yank a big ol' trout out of Lake Brittle with an acceleration of 1.5 m/s 2 using very light fishing line that has a small tensile force. They unfortunately lose the fish as the line snaps but estimate the mass of the trout to be 1.2 kg. What was the force on the fishing line?

Force due to Gravity Bill, the weightlifter, lifting in the Patriot weight room is bench pressing 245 pounds. (2.2 pounds = 1 kg) Bill exerts a force of 1010 N in lifting the weight. What is the acceleration of the weight? Physics Name: _______________ Block: ___ Date: ______ Physics Name: _______________ Block: ___ Date: ______

Force due to Gravity A mob snitch is taken up in an airplane to be disposed of, if the person has a mass of 120 kg and they tie a 50 kg weight to him, what is his velocity after 3.5 seconds, if the upward drag force acting against him is 225 N?

Force due to Gravity

Solving Force Problems In addition to Atwood’s Machine problems and inclined plane problems another common force problem involves elevators. When a person stands on a scale in a motionless environment (acceleration is zero) the scale reading gives his normal weight (the effect of gravity on his mass that is mass x gravity - remember w = mg) When a person stands on a scale in a moving environment the scale still gives his normal weight if the motion is at a constant velocity that is acceleration is still zero. If, however, the system is accelerated upwards or downwards, the scale reading changes and his normal weight is not the scale reading !

Solving Force Problems If the system is accelerating upwards, the scale must support the weight of the individual and also provide additional force to accelerate the person upwards. The scale reading therefore is greater than the normal weight of the person. If the system is accelerating downwards, the scale must provide a reading less than the normal weight since if is provided an upward force equal to the weight the net force would be zero and no acceleration would occur ! The extreme example of this situation would be when both the person and the scale are in free fall. In this case, no upward force is supplied by the scale and its reading is zero. The acceleration of both the person and scale then is that of gravity (- 9.8 m/s 2 )