Engineering Statics · Trusses, frames, and machines
A thin plate occupies the region bounded by y = √x, y = 0, and x = 9 (x and y in inches)
Problem
A thin plate occupies the region bounded by y = √x, y = 0, and x = 9 (x and y in inches). The plate has constant thickness but areal density ρ_A = (1 + 0.1x) oz/in². Determine the center of mass (x̄, ȳ) of the plate.
Hint
Because ρ_A depends only on x, use vertical strips and mass (not area) moments.
Check your work
Work the problem yourself first. Then open it in Training to check your answer and read the full worked solution.
The answer check and full solution for this problem come with ProofAnvil Practice membership ($19 USD monthly). See membership. Or start with the free Engineering Statics sample problem: Try the free sample problem.
More Engineering Statics practice problems
- A force of magnitude 480 N acts through the origin in the direction of the vector 3i −…Vectors, moments, couples, and equivalent force systems
- Resolve the 1.5 kN force that acts from P(2 m, −1 m, 2 m) to Q(−1 m, 3 m, 0) into a…Vectors, moments, couples, and equivalent force systems
- Beam QR of length 5.2 m is supported by a roller at Q and a pin at RParticle and rigid-body equilibrium
- A pliers-type cutting tool has handles OA and OB of length 180 mm pivoted at O, and…Particle and rigid-body equilibrium
- A clutch plate transmits torque through dry frictionTrusses, frames, and machines
- A T-section is built from a 140 mm × 20 mm flange centered on the y-axis with its top…Distributed loads, centroids, and resultants
- A parabolic cable under uniform horizontal loading of intensity w₀ = 2.10 kN/m spans L…Distributed loads, centroids, and resultants
- A pushed block tips before it exhausts static frictionDry friction and impending motion
- Four supporting cable segments give an ideal four-to-one block tacklePotential energy and virtual work