Answer to Question #89709 in Mechanics | Relativity for Rawail Ahmed

Question

Q) A model car, of mass 1.5 kg. with a string attached to its upper end, is placed on a slope as shom,ii in the diagram. The force in the string, parallel to the slope, needed to move the car up the slope at a constant velocity is 10 N.
(i) Describe, with the aid of a diagram, how the force in the string can be measured

Answer 1

Look at the figure:

Assume there is no friction and the incline is at the angle $\alpha$ above the horizontal. We see that since the car moves with constant velocity, according to Newton's second law, the sum of all three forces is 0, i.e. the sum of projections of the forces on the incline (x-axis) is 0, and the sum of projections of the forces on y-axis (perpendicular to the incline) is 0 as well:

$$Ox:\space -P+mg\text{sin}\alpha=0,$$ $$Oy:\space N-mg\text{cos}\alpha=0.$$

Hence the force in the string can be measured is we weigh the car and measure the angle of incline:

$$P=mg\text{sin}\alpha.$$

Or you can simply take a spring balance, attach it to the string and if is measures mass in kilograms, multiply the measured mass by 9.8 to get force in newtons.