Work Done By Friction In Stopping A Moving Object

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{3}A_{31} Base Sequence = 12735 String Sequence = 12735 - 3 - 31 **

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Work Done By Friction In Stopping A Moving Object

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A luggage weighing 490 lbs is being moved on a horizontal conveyor belt at 6 miles per hour. The conveyor is then brought to an abrupt stop. The luggage then slided for 1.37 secs during which time it covered 6 feet before coming to a complete stop.

(a) Calculate the work done by friction in bringing the luggage to a complete stop. The coefficient of friction between conveyor belt and luggage is 0.2.

(b) Confirm that the distance covered during the slide and the duration of the slide are 6 feet and 1.37 secs respectively.

**The string**:

(a) S_{7}P_{3}A_{31} (Force - Pull).
**The math**:

Pj Problem of interest is of type *force*. Work problems are generally of type *force* because *force* is the *doer* of *work*. In the case of *white-collar work*, *intellectual force* actuates *materiality*.

Consider the above diagram (FW.1):

Let W be the work done by friction to stop the moving object.

When conveyor belt is stopped abruptly, the only force acting to bring the motion of the luggage to a stop is the friction force between the luggage and the belt. This friction force is equal to the weight of the luggage. The work done by friction is equal to the kinetic energy of luggage before conveyor belt was abruptly stopped.

Speed of conveyor belt = 6 miles/hr = 8.8 ft/sec

Mass of luggage = 490/32 = 15.31 lbs

So, Kinetic Energy = (mv^{2})/2 = (15.31 x 8.8 x 8.8)/2 = 592.8 ft-lbs.

So, W = kinetic energy = 592.8 ft-lbs.

(b) Strings are: S_{7}P_{4}A_{41} (Linear motion) and S_{7}P_{5}A_{51} (Physical Change - Duration) respectively.

To calculate distance assuming it was not given, we equate kinetic energy with work done by friction

So, 592.8 = (friction force) x distance

So, 592.8 = μ490 x distance = 0.2 x 490 x distance

So, distanced luggage slided = 592.8/98 = 6 feet.

To calculate duration of slide assuming it was not given, we use the *impulse momentum formula*:

R x t = m(v_{f} - v_{o}).

R is the resultant force, t is time the resultant force is acting on the luggage, m is mass of the luggage, v_{f} is the luggage's final velocity and v_{o} is the luggage's original velocity.

So, R = friction force = -98 lbs; m = 490/32; v_{o} = 8.8 ft/sec; v_{f} = 0.

So, -98t = (490/32)(0 - 8.8)

So, t = 1.37 secs.

In SI units: mass is in kilograms, distance is in meters, velocity is in meters/sec, acceleration is in meters/sec^{2}, force is in Newton and work is in Joules.

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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