Car parked on hill?

Question

The answer is the letter or letters indicating EACH choice that forms a correct statement.

A car is parked on a hill
(a) the weight of the car acts vertically downward
(b) a component of the weight acts perpendicular to the surface of the hill
(c) a component of the weight acts parallel to the surface of the hill
(d) both the perpendicular and parallel components act to move the car down the hill

Answer 1

Nice question --- it makes you THINK about each possibility, rather than the usual kind of multiple choice question which students often tackle merely by crossing out whatever a "hunch" tells them couldn't be the answer.

I briefly give the reasons, following each answer, although not explicitly requested. Let the car's mass be 'M,' the downward acceleration vertically of freely moving objects near the Earth's surface be 'g,' and the angle of the hill's surface above the horizontal be 'theta', so that the mathematical "slope" 'm' in y = m x + const. is tan (theta), the VERTICAL RISE per unit HORIZONTAL displacement. (In fact, in some countries road signs display what amounts to sin[theta]: the VERTICAL RISE per unit length of ROAD TRAVERSED.) Then:

a. is TRUE (weight is Mg)
b. is TRUE (perpendicular component is Mg cos[theta])
c. is TRUE (parallel component is Mg sin[theta])
d. is FALSE --- only the PARALLEL component Mg sin(theta) acts to move the car down the hill; the other one is simply "pressing" the car into the road's surface.

So the answer, in letters only, is a, b, c.

Live long and prosper.

Answer 2

(a) (b) (c) are true
(d) is false

a component of the weight acts parallel to the surface of the hill => m.g.Sin x

a component of the weight acts perpendicular to the surface of the hill => m.g.Cos x

the weight of the car acts vertically downward => W=mg

Answer 3

Very nice Answer