Question

homework 3 begin date: 8/17/2025 11:59:00 pm due date: 9/9/2025 11:59:00 pm end date: 9/9/2025 11:59:00 pm
problem 8: (6% of assignment value)
a toy car rolls down a ramp at a constant velocity. the car’s mass is m = 1.2 kg, and the ramp makes an angle of θ = 11° with respect to the horizontal. assume that the rolling resistance is negligible. note the coordinate system provided on the image where the x axis is parallel to and directed down the incline.

• part (a) ✔

what is the magnitude, in meters per squared second, of the car’s acceleration?
a = 0.000 m/s² ✔ correct!

• part (b) ✔

what is the numeric value, in newtons, for the sum of the forces in the x direction?
σ fₓ = 0.000 n ✔ correct!

• part (c)

assuming the car experiences only air resistance, with magnitude fᵣ, in opposition to its motion. write an expression for the sum of the forces in the x direction using the acceleration due to gravity, g, and the variables provided.
ς fₓ =

Explanation:

Step1: Identify forces in x - direction

The forces acting on the car in the x - direction (down the incline) are the component of the gravitational force and the air resistance. The component of the gravitational force along the x - direction is $F_{g,x}=mg\sin\theta$, and the air resistance $F_r$ acts opposite to the motion (so in the negative x - direction if we take down the incline as positive x).

Step2: Apply Newton's second law

According to Newton's second law, $\sum F_x = F_{g,x}-F_r$. Substituting $F_{g,x}=mg\sin\theta$ into the equation, we get $\sum F_x=mg\sin\theta - F_r$.

Answer:

$\sum F_x = mg\sin\theta - F_r$