A 70 kg cart is pushed for 50 m with a constant velocity upon a 45º frictionless incline. What is the work done on the cart?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Work is defined as force through a distance:

1) Work = Force * Distance, or  W=fd

The cart has a mass of 70 kg, subject to the acceleration of gravity, 9.8 m/sec^2.

Force is defined in terms of Newtons (N) as (kg m)/sec^2, so the cart has a force of

...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

Work is defined as force through a distance:

1) Work = Force * Distance, or  W=fd

The cart has a mass of 70 kg, subject to the acceleration of gravity, 9.8 m/sec^2.

Force is defined in terms of Newtons (N) as (kg m)/sec^2, so the cart has a force of

70kg * 9.8 m/sec^2 = 686 (kg m)/sec^2 or 686 N

so by formula 1, the Work should be 686N * 50m, however, there's an incline to consider which modifies the force.  Formula 1 is better described as:

2) Work = Force * Distance(cos (theta)), where theta is the angle of the incline.  So the formula should read:

Work = 686N * 50m(cos 45)

=  686N * 50m(.7071)

=  686N * 35.355m

=  24253 Nm

A Newton * meter (Nm) is the same thing as a Joule (J), which is used to express an amount of work, so

=  24253 J

 

Approved by eNotes Editorial Team