Do Not Make This $20,000 Mistake - Part 1

Calculus Level 2

Ganesh forgot to set the brake on his car, and watched in horror as it rolled down a steep $65^\circ$ incline slope and was completely smashed. The mechanic attached a metal cable to the body of the car in order to haul it up the slope.

If the automatic winch draws the cable in at a constant rate, which of the following describes the speed at which Ganesh's car will be pulled up the slope?

Speed increases over time Speed varies with time, no simple description Speed decreases over time Speed is constant

5 solutions

Yo Baba
Apr 10, 2014

we can do it by string constraint which says that each and every point on a string performs similar motion(accelerated, uniform , non-uniformly accelerated ,etc.) here, the cable is being wound up by at a constant rate i.e. the points of the cable will have a constant speed for moving up and thus the piont of the cable in contact with the car will move up with constant speed and thus, the car moves up the plane with a constant speed.(for ideal conditions ) and an explanation that is valid for all conditions is given by mr. Prashik Khadse "Constant RPM is expected to give constant speed only" as the rpm or we can say it the rate of winding of the cable by the winding mechanism the angular speed of the rotor of the winding mechanism will be constant so speed(angular speed xradius) will be constant and then the above explanation is applicable hope this helps somebody!:)

As the car is pulled up more cable is wrapped on the winch, which increases the radius. Thus the speed increases.

Allen Bradley - 7 years, 2 months ago

Nicely explained!

Anuj Shikarkhane - 6 years, 11 months ago

Prashik Khadse
Apr 10, 2014

Constant RPM is expected to give constant speed only

my idea was that the velocity will increase by constant rate because the car will acquire a constant acceleration due to constant tension force over the time ! .. but i still dun get how the velocity of the car will be constant !

Ahmad Samir - 7 years, 2 months ago

The tension force must balance other forces such as gravity and friction so speed remains constant.

Steven Perkins - 7 years, 2 months ago

you're right but if we applied Newton's law that the sum of forces in the inclined plane direction will equal the mass*the acceleration then we get a constant acceleration which means constant increasing in velocity ! .. something wrong with this ? or i couldn't understand what you mean in a right way ? :)

Ahmad Samir - 7 years, 2 months ago

@Ahmad Samir – Once the cable is moving at a constant velocity, the forces are balanced, that is, the net force is 0. So no acceleration.

We know there is no acceleration because the velocity is constant. The only thing moving the car is the cable, which we're told is moving at a constant velocity. Hope that helps.

Steven Perkins - 7 years, 2 months ago

Ali Baqar
Apr 11, 2014

There evolves two situation from the statement of the problem. Firstly, if 'constant rate' means equal length cable being drawn in ever second, then yes the last choice of answer is correct. But theoretically speaking, if 'constant rate' means constant rate of spin of the winch then the answer becomes different because with every turn of the winch the diameter of the 'reel' increases as the the cable is wound on it and the rate at which the cable is drawn in will increase. Although, I selected the last answer.

Wooil Jung
Sep 21, 2014

it tells you the acceleration is 0. this means there will be no change in speed nor velocity. so yeah.

Zain Ashfaq
Jun 14, 2014

velocity of car will be constant because velocity depend on time and displacement v=d/t hence car is strecheing by constant rate so its displace will be also constant hence velocity remain constant in this case

how it can be constant since there is force static frictional force when the car start moved on

Antoni Ho - 6 years, 8 months ago

Do Not Make This $20,000 Mistake - Part 1

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