while moving

Mass (m) = kilograms, kgDistance (s) = meters, mTime (t) = seconds, s

Weight = m*g (Newtons)

1 Mg = 1000 kg

T T

(3Mg)(9.81m/s2) )(Cos 30o) – (3)(9.81) kN = (3 Mg)(ay) = (3 Mg)(2/3 m/s2) T = 18.1 kN

30o

Quiz 1 - Dynamics – Fall 2011 Name _________________________________Calculator in degrees!

Units FPSMass = Slug, SlugDistance = feet, ftTime = seconds, s

Weight = mg (pounds)

The 1 slug mass rotates around the vertical pole in a horizontal circular path. The angle θ = 30o and the length of the string L = 4 ft. What is the tension in the string? What is the magnitude of the velocity of the mass? Show all views, coordinate systems and a free-body diagram.

n

t

Top view

30on

y

Back view

T

mg

Quiz 2 - Dynamics – Fall 2011 Name _________________________________Calculator in degrees!

The spring has a stiffness of 200N/m and a free length of 0.1 m. The 25 kg block is installed at rest at A. The surface is smooth. Use work and energy to find the velocity of the block when s = 0.4 m

0.5m

Quiz 3 - Dynamics – Fall 2011 Name _________________________________

∑U 1−2=T2−T1

UF + Uspring = 12mv2

2- 12mv1

2

Fs - ½ k (x22 – x1

2) = 12mv2

2- 12mv1

2

(100 kgms2

)(0.4m) −12 (200

kgms2

m )[(0.4m)2−(0.2m)2 ] = 12(25 kg)v2

2 - 0

v2 = 1.50 m/s

The winch on the back of the Jeep A is turned on and pulls in the tow rope at 2 m/s measured relative to the Jeep. If both the 1.25 Mg car B and the 2.5 Mg Jeep A are free to roll, determine their velocities at the instant they meet. If the rope is 5 m long, how long will this take? Since these are internal forces, use conservation of momentum and relative velocity

Quiz 4 - Dynamics – Fall 2011 Name _________________________________

mA v1 A+mB v1B=mA v2 A+mB v2 B

0+0=2500kg v2A+1250 kgv2 B v2B=−2v2 A

v⃗B= v⃗ A+ v⃗B /A

−2 v2 A=v2 A−2m/ sv2A=0.667m /sv2B=−1.33m /s

s = v t5 m = 2 m/s ( t)t = 2.5 s

2. (25 Pts) The pendulum ball has a mass of 30kg and a speed of 4 m/s at the instant it passes the lowest point, θ = 0o. a) Use work and energy to find the velocity when θ = 20o. b) Find the tension in the cord at the 20o angle.

4m/s

Midterm Test - Dynamics – Fall 2011 Name _________________________________

1 (25 Pts) The crate has a mass of 120 kg and the kinetic coefficient of friction is μk = 0.5. If the tension in the cable is 1200 N, find the acceleration of the crate.

3. (25 Pts) The 2 kg ball is thrown at the suspended 20 kg block with a velocity of 4 m/s. a) If the coefficient of restitution between them is e = 0.8, determine the velocity the block moves out of the collision. b) If the time of impact is 0.005 s, find the average normal force exerted on the block.

F t

4. (25 Pts) If the hydraulic cylinder shortens at a constant rate of vC = 2 ft/s, determine the angular velocity of the link ACB and the velocity of block B at the instant shown.

Midterm Test - Dynamics – Fall 2011

The trailer with its load has a mass of 150 kg and a center of mass at G. It is subjected to a horizontal force of 600N. Determine the trailer’s acceleration and the normal force on the pair of wheels at A and B. The wheels are free to roll and have negliable mass. (must show free-body diagram)

Quiz 5 - Dynamics – Fall 2011 Name _________________________________

Quiz 6 - Dynamics – Fall 2011 Name _________________________________

400N

3m

0.5mA

Quiz 7 - Dynamics – Fall 2011 Name _________________________________

The uniform slender rod has a mass of 100 kg. When the 400 N force is applied from rest, the base slips (μk = 0.25). Find the angular acceleration of the rod and the linear acceleration of the base, A

Quiz 8 - Dynamics – Fall 2011 Name _________________________________

Determine the angular velocity of the two 10 kg rods when θ = 180o if they are released from rest in the position θ = 60o.Show sketchs for positions 1 and 2.

Quiz 9 - Dynamics – Fall 2011 Name _________________________________

The flywheel A has a mass of 30 kg and a radius of gyration of kC = 95 mm. Disk B has a mass of 25 kg, is pinned at D, and is coupled to the flywheel using a belt which does not slip. If the motor supplies a counterclockwise moment of M = 25 Nm, find the angular velocity of the disk 3 s after the motor is turned on from rest.

Exam - Dynamics – Fall 2011 Name _________________________________

1. (20 pts)The 20 kg punching bag has a radius of gyration about its center of mass, G of kG = 0.4m. If it is initially at rest and is subjected to a horizontal force of F = 30 N (not impact), use relative acceleration to determine the initial linear acceleration of the top of the bag, B. G

Exam - Dynamics – Fall 20112. (22 pts)The 100 lb uniform rod is at rest in a vertical position when the cord attached at B is subjected to a force of P = 50 lb. Find the rod’s initial angular acceleration and the reactive force that pin A exerts on the rod.

0.5ft

0.4ft

Exam - Dynamics – Fall 2011

3. (22 pts) The gear has a weight of 15 lb and a radius of gyration of kG = 0.375 ft. If the spring is unstreteched when the torque M = 6 lb ft is applied, determine the gear’s angular velocity after its center of mass has moved to the left s = 2 ft. (spring constant 3 lb/ft)

P=25 lb

0.75ft

2ft

60lb

Exam - Dynamics – Fall 2011

4. (20 pts)The spool has a weight of 75 lb and a radius of gyration kO = 1.2 ft. If the cylinder weighs 60 lb and a force P = 25 lb is applied to the cable from the motor, determine the speed of the cylinder in 5 s starting from rest. (use impulse)

Exam - Dynamics – Fall 2011

5. (16 pts)The fan has a mass of 25 kg and is fixed to the end of a horizontal beam that has a negilible mass. The fan blade is mounted eccentrically on the shaft such that it is equivalent to and unbalanced 3.5 kg mass located 100 mm from the axis of rotation. If the static deflection of the beam is 50 mm as a result of the weight of the fan, determine the amplitude of the steady-state vibration of the fan if the angular velocity of the fan blade is 10 rad/s.