Engineers measure the torque applied by an automated actuator at several equally…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
Engineers measure the torque applied by an automated actuator at several equally spaced angular positions as it opens a valve. The data are recorded in the table below.
θ (rad) | 0.0 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0
τ (Nm) | 5.0 | 4.2 | 3.1 | 1.8 | 0.4 | -0.9
Positive torque acts to open the valve. The actuator starts at θ=0 and stops at θ=1.0rad.
(a) Using the trapezoidal rule and the data provided, estimate the work done by the actuator in opening the valve from θ=0 to θ=1.0rad. Show all calculation steps and include units.
(b) Explain how your answer in part (a) relates to the physical meaning of the area under a torque-versus-angle graph.
(c) Suppose an analytical model predicts that the torque should vary according to τ(θ)=5.1−6.0θ (with τ in Nm and θ in rad). Determine the exact work predicted by this model over the same angular range and compare it with your trapezoidal estimate. Compute the percent difference.
(d) Discuss two possible reasons—one experimental and one mathematical—why the numerical estimate in part (a) might differ from the analytical value in part (c).