Final answer:
The acceleration of a Goliath beetle down a frictionless slope is found using the parallel component of gravitational force and Newton's second law, yielding an acceleration of approximately 5.9 m/s².
Step-by-step explanation:
The question involves calculating the acceleration of a Goliath beetle down a frictionless slope in a physics context. First, we need to identify the forces acting on the beetle. The gravitational force can be broken down into two components: one parallel to the slope and one perpendicular to it. The perpendicular component only contributes to the normal force and does not affect the beetle's motion down the slope; hence it can be ignored due to the lack of friction. The parallel component is what causes the beetle to accelerate.
Let's denote the mass of the beetle as 'm' (0.080 kg), the acceleration due to gravity as 'g' (9.81 m/s²), and the angle of the slope as θ (37.0 degrees).
The parallel component of the gravitational force (Fparallel) is given by: Fparallel = m × g × sin(θ)
According to Newton's second law, the beetle's acceleration (a) is:
a = Fparallel / m
Plugging in the values, we get:
a = (0.080 kg) × (9.81 m/s²) × sin(37.0 degrees) / 0.080 kg = 9.81 × sin(37.0 degrees) m/s²
Using a calculator:
a ≈ 5.9 m/s²
Therefore, the acceleration of the beetle along the slope is approximately 5.9 m/s².