EGR 280 – Mechanics Exam

Statics of particles and rigid bodies

∑F = R = 0and∑MO = 0MO = rO×F

g = 9.81 m/s2 = 32.2 ft/s2

Normal stress, deformation

σ = P/Aε = δ/Lσ = Eεδ = PL / AE

Friction

static equilibrium: f ≤ μsN ; if moving, f = μkN

belt friction: T2 = T1 eμβ

Particle kinematics

v = dx/dta = dv/dt = d2x/dt2 = v(dv/dx)

uniform rectilinear motion: x = x0 + v0t

uniformly accelerated rectilinear motion:

v = v0 + a0tx = x0 + v0t + ½ a0t2v2 = v02 + 2a0(x-x0)

relative motion: xB = xA + xB/AvB = vA+ vB/AaB = aA + aB/A

intrinsic coordinates: v = v eta = dv/dt et + v2/ρ en

Particle kinetics

Newton’s Second Law:∑F = ma

intrinsic coordinates:∑Ft = m dv/dt∑Fn = m v2/ρ

work and energy:TA + UAB = TB

kinetic energy:T = ½mv2

work done by spring:U = ½k δ2 ; by weight: -Wy

conservation of energy:VA + TA = VB + TB

if not conserved, then:VA + TA = VB + TB + energy lost

impact and momentum:mv1 + ∫Fdt = mv2

coefficient of restitution:e = (v´B-v´A)/(vA-vB) = v´B/A/vA/B

Rigid body kinematics – plane motion

translation:vA = vBaA = aB

rotation:v = ωk × r a =αk × r – ω2r

uniform rotation: θ = θ0 + ω0t

uniformly accelerated rotation:

ω = ω0 + α0tθ = θ0 + ω0t + ½ α0t2ω2 = ω02 + 2α0(θ-θ0)

general plane motion:vB = vA +ωk × rB/Aa= aA + αk × rB/A – ω2rB/A

rolling:v = ωra = αr

pulleys:ω1r1= ω2r2gears: ω1r1= -ω2r2

mass moments of inertia:

parallel axis theorem: IO = IG + md2 ; radius of gyration: k2 = I/m

rod: IG = mL2 / 12disk: IG = mr2 / 2

ring: IG = mr2sphere: IG = 2mr2 / 5

Rigid body kinetics – plane motion

Newton’s Second Law: ∑F = ma∑MG = IGαk

non-centroidal rotation: ∑Mo = Ioαk

kinetic energy:T = ½mvG2 + ½ IGω2 ; non-centroidal rotation: T = ½ IOω2

total momentum:mvG + IGω ; non-centroidal rotation: Ioω

  1. Given force F = (3i + 5j + 4k)lb passing through point (4,12,6)ft, find the y-component of the moment of F about the origin.
  2. -2 ft-lb
  3. 0
  4. 2 ft-lb
  5. 14 ft-lb
  1. Given F = (3i + 5j + 4k)N and r = (6i – 3j + 12k)m, find F∙r.
  2. -21 N-m
  3. (-72i + 12j + 39k)N-m
  4. 42 N-m
  5. 51 N-m
  1. The block shown is acted upon by a force P = 7 lb. If μs=0.8 and μk=0.5, determine the acceleration of the block.
  2. 0
  3. 3.22 m/s2
  4. 6.44 m/s2
  5. 25.8 m/s2
  1. Determine the force in member AB.
  2. 900 N (T)
  3. 900 N (C)
  4. 1200 N (T)
  5. 1200 N (C)
  1. The reaction at B is:
  2. 3.5 lb ↑
  3. 3.5 lb ↓
  4. 16.5 lb ↑
  5. 16.5 lb ↓
  1. Find the force in member BD of the simple truss.
  2. 750 N (C)
  3. 1000 N (C)
  4. 1000 N (T)
  5. 3000 N (C)
  1. A block will slide down a 30° incline if the coefficient of static friction is less than
  2. 0.500
  3. 0.577
  4. 0.866
  5. 0.625
  1. What force F is required for equilibrium?
  2. W / 4
  3. W / 6
  4. W / 8
  5. W / 9
  1. One complete revolution of a rope about a post is used to hold a boat. If μs=0.5, what maximum force by the boat can be resisted if the holder provides a force of 100N?
  2. 962 N
  3. 1920 N
  4. 2310 N
  5. 3850 N
  1. A 30-mm diameter rod supports a tensile force of 35 kN. What is the normal stress in the rod?
  2. 12.4 MPa
  3. 36.4 MPa
  4. 42.8 MPa
  5. 49.5 MPa
  1. A weight of 40 kN is suspended from a 20-m long, 20-mm diameter steel cable. If E = 207 GPa, determine the elongation of the cable.
  2. 3.1 mm
  3. 8.7 mm
  4. 10.8 mm
  5. 12.3 mm
  1. The Work and Energy principle is a relationship between
  2. Force, acceleration and time
  3. Force, speed and distance
  4. Force, velocity and time
  5. All of the above
  1. Impulse and Momentum is a relationship between
  2. Force, acceleration and time
  3. Force, speed and distance
  4. Force, velocity and time
  5. All of the above
  1. A ball is given an initial velocity of 40 m/s straight up. Ignoring friction, how high will the ball go?
  2. 40 m
  3. 60.8 m
  4. 81.6 m
  5. 122 m
  1. A wheel rotates at 20 rad/s. How many revolutions will it rotate in 4 s, after it begins to decelerate at 10 rad/s2?
  2. 3.18 rev
  3. 4.25 rev
  4. 6.37 rev
  5. 7.40 rev
  1. A car is traveling at a constant speed around a circular curve having a radius of curvature of ρ = 250 m. If the magnitude of the car’s acceleration is 1.5 m/s2, determine the speed at which the car is traveling.
  2. 19.4 m/s
  3. 23.7 m/s
  4. 32.8 m/s
  5. 34.1 m/s
  1. The center of the wheel is moving to the right with a speed of 2 m/s. If no slipping occurs at the ground, determine the velocity of point B at the instant shown.
  2. 1.33 rad/s cw
  3. 4 m/s →
  4. 3 m/s →
  5. 2 m/s →
  1. If the system shown is released from rest, find the tension in the cord which is wrapped around the 50-kg cylinder.
  2. 80 N
  3. 99 N
  4. 100 N
  5. 109 N
  1. The 20-kg mass in Problem 18 drops from rest. If it falls through 2 m, what is the angular speed of the cylinder?
  2. 8.4 rad/s
  3. 9.3 rad/s
  4. 10.4 rad/s
  5. 12.2 rad/s
  1. The 35-kg block strikes the unstretched spring. The maximum deflection of the spring is:
  2. 1.67 m
  3. 2.80 m
  4. 4.78 m
  5. 6.33 m
  1. The 6-lb ball is fired from rest using a spring as shown. Determine how far the spring must be compressed so that when the ball reaches a height of 8 ft it has a speed of 6 ft/s.
  2. 0.80 ft
  3. 1.27 ft
  4. 1.60 ft
  5. 2.56 ft
  1. A ball is dropped vertically downward onto a horizontal surface from a height of 52 m. If the coefficient of restitution e = 0.8, determine the speed of the ball after it bounces.
  2. 20.5 m/s
  3. 25.6 m/s
  4. 30.6 m/s
  5. 32.0 m/s
  1. The clock pendulum consists of a 1-kg slender rod A and a 4-kg moveable disk B. Determine the mass moment of inertia of the pendulum about the fixed point O.
  2. 0.10 kg-m2
  3. 1.97 kg-m2
  4. 2.30 kg-m2
  5. 3.14kg-m2

  1. In the belt and pulley system shown, if pulley Ais rotating at 1740 rpm, what is the angular speed of pulley D? Pulley C is attached to and rotates with pulley B.
  2. 196 rpm
  3. 870 rpm
  4. 1390 rpm
  5. 2180 rpm
  1. In the gear system shown, if gear A is rotating at 1740 rpm clockwise, determine the angular velocity of gear E. Gear B is attached to and rotates with gear C.
  2. 61.9 rpm ccw
  3. 61.9 rpm cw
  4. 96.7 rpm ccw
  5. 96.7 rpm cw