Net Force on 1.6t Car on 40o Banked Icy Road

[chem_is_lovex]

Homework Statement

what is the net force acting on a 1.6t car initially parked on a smooth icy road banked at 40^o. (frictional forces are negligible)

Homework Equations

Fd=mgsin$$\theta$$

The Attempt at a Solution

I'm not too sure.
1600 x 9.8 x sin40

but it = the wrong number?? help!

 

[berkeman]

Homework Statement

what is the net force acting on a 1.6t car initially parked on a smooth icy road banked at 40^o. (frictional forces are negligible)

Homework Equations

Fd=mgsin$$\theta$$

The Attempt at a Solution

I'm not too sure.
1600 x 9.8 x sin40

but it = the wrong number?? help!

I believe you at least have a problem with units. What is the "ton" thing in terms of mks units? It's good to get in the habit of carrying units along in your equations, and multiplying and dividing them out just like you are doing with the numbers. If you are calculating a force in mks units, the answer's units had better be in kg*m/s^2, right?

 

[nlightner]

I would approach this problem by first identifying all the forces acting on the car. In this case, the only force acting on the car is its weight (mg) which can be broken down into two components: the normal force (N) perpendicular to the surface of the road, and the force due to gravity (mg) acting parallel to the surface of the road. Since the road is banked at an angle of 40 degrees, we can use trigonometry to determine the magnitude of these components.

The normal force (N) is equal to the weight of the car (mg) multiplied by the cosine of the angle of the bank (40 degrees). This gives us a value of 1600 x 9.8 x cos40 = 12,249.49 N.

The force due to gravity acting parallel to the surface of the road is equal to the weight of the car (mg) multiplied by the sine of the angle of the bank (40 degrees). This gives us a value of 1600 x 9.8 x sin40 = 8,199.66 N.

Since the frictional forces are negligible, the net force acting on the car is simply the force due to gravity (8,199.66 N) since there are no other forces acting in the horizontal direction.

Therefore, the net force acting on the 1.6t car on the 40 degree banked icy road is 8,199.66 N. It is important to note that this net force is not causing the car to move, but rather keeping it in equilibrium on the banked surface. Any additional force, such as a push or a strong gust of wind, could cause the car to move.