Final answer:
To find the work done by the nonconservative force of the track on the toy car, one must calculate the change in kinetic and gravitational potential energy using the car's mass, the drop in height, and the change in speed. This requires converting units to standard SI units and applying the work-energy principle.
Step-by-step explanation:
To calculate the work done by the nonconservative force of the track on the toy car, we must consider the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy plus the change in its gravitational potential energy.
First, we need to convert the mass of the car from grams to kilograms, which is 0.127 kg, and the drop in height from centimeters to meters, which is 0.569 m. The initial and final speeds of the car are given as 1.38 m/s and 4.90 m/s, respectively.
The change in kinetic energy (ΔKE) is calculated as:
ΔKE = (1/2) m v_f^2 - (1/2) m v_i^2
where m is the mass of the car, v_f is the final speed, and v_i is the initial speed. Substituting the values, we get:
ΔKE = (1/2) × 0.127 kg × (4.90 m/s)^2 - (1/2) × 0.127 kg × (1.38 m/s)^2
Calculating this gives us the change in kinetic energy. The change in gravitational potential energy (ΔPE) is:
ΔPE = mgh
where g is the acceleration due to gravity (9.81 m/s^2), and h is the height change. Using the given values:
ΔPE = 0.127 kg × 9.81 m/s^2 × 0.569 m
Since the work done by gravity is negative (as it acts opposite to the direction of motion), the total work done by the nonconservative force equals the sum of the changes in kinetic and potential energy:
Work_nonconservative = ΔKE + ΔPE
Add these values together to find the total work done by the nonconservative force in joules.