The Special Olympics raises money through "plane pull"...

The Special Olympics raises money through "plane pull" events in which teams of 25 people compete to see who can pull a $74,000 \mathrm{kg}$ airplane $3.7 \mathrm{m}$ across the tarmac. The inertia of the plane is an issue-but so is the $14,000 \mathrm{N}$ rolling friction force that works against the teams. If a team pulls with a constant force and moves the plane $3.7 \mathrm{m}$ in $6.1 \mathrm{s}$ (an excellent time), what fraction of the team's work goes to kinetic energy and what fraction goes to thermal energy?

Key Concepts

Constant Acceleration Kinematics

When a constant net force is applied, an object experiences constant acceleration. Kinematics formulas are then used to relate displacement, time, acceleration, and final velocity, which in turn allows for the calculation of kinetic energy and the work done by friction.

Friction and Energy Dissipation

Friction is a non-conservative force that opposes motion, converting mechanical energy into thermal energy. In dynamics problems, the work done against friction is not recovered as kinetic energy but is instead dissipated as heat.

Work-Energy Theorem

This principle states that the net work done on an object is equal to its change in kinetic energy. It is used to analyze how energy is transferred into kinetic energy when forces are applied, taking into account both energy gained as motion and energy lost to opposing forces, such as friction.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion, calculated as one half the mass multiplied by the square of its velocity. In problems involving work, it represents the portion of energy that goes into accelerating an object.

Transcript

0:00 High.

00:01 In the given problem, suppose the total force applied by all the 25 people on this plane is f.

00:26 Then the total work done by the people total work done will be converted into two forms.

00:38 One, in the form of kinetic energy.

00:43 Of the plane as it will start moving and another work done in the form of work done against rolling friction as the distance traveled is d as the distance traveled by the plane distance moved under the applied force by the plane if supposed to be d then the total work done will be f into d which we are saying will be converted into kinetic energy means half mv square plus small f where this is small f is the force of friction into d.

01:40 So this is this f into d is the work done by the force of friction.

01:49 Now we have to find this v finally speed.

01:53 So to find this final velocity for the time being we make it equation number one.

01:59 Now using first equation of motion.

02:04 Now using first equation of motion which says this v is equal to u plus a t.

02:14 V is the final speed achieved by the plane after moving this distance of 3 .7 meter in 6 .1 seconds.

02:22 U is the initially speed which was 0 acceleration this is not given to us and time t which is 6 .1 second.

02:33 We will use it later on.

02:35 Now the net force acting on the plane will be the applied force in the forward direction, capital f, and force of friction in the backward direction.

02:47 So total force will be f minus f and using newton's second law of motion that may be equated with m into a.

03:00 So acceleration here comes out to be f minus f by m.

03:05 M.

03:06 M is a.

03:06 The mass of the plane...

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