Question

Construct Your Own Problem: Two people push a toboggan with children uphill on a snow-covered slope. Create a problem calculating the acceleration of the toboggan and its load. Include a free-body diagram and consider forces, slope angle, and masses.

a) Acceleration depends only on the forces exerted
b) Acceleration is independent of the slope angle
c) Acceleration is affected by frictional force
d) Acceleration is inversely proportional to mass

Answer 1

To solve this problem, we consider the forces acting on the toboggan and apply Newton's second law. We calculate the components of the gravitational force and then determine the net force to find the acceleration.

Step-by-step explanation:

Construct Your Own Problem: Calculating Toboggan Acceleration

Let's consider two people pushing a toboggan, with the toboggan and four children having a combined mass of 120.0 kg, up a snowy slope of 25°. The combined force exerted by the two people pushing is 300 N, and the frictional force opposing the motion is 60 N. We need to calculate the acceleration of the toboggan.

To construct the free-body diagram, we first identify all the forces acting on the toboggan:

• Gravitational force (Fg)
• Normal force (N)
• Force exerted by the people (Fp)
• Frictional force (Ff)

We resolve Fg into components parallel and perpendicular to the slope. The parallel component (Fg||) causes the toboggan to slide down, while the perpendicular component (Fg⊥) is balanced by the normal force. Using trigonometry, Fg|| = m × g × sin(θ) and Fg⊥ = m × g × cos(θ).

By applying Newton's second law (F = m × a) and considering the forces parallel to the slope, we get:

Fp - Fg|| - Ff = m × a

Substituting the known values:

300 N - (120.0 kg × 9.8 m/s2 × sin(25°)) - 60 N = 120.0 kg × a

After calculating the values, we can solve for a.