Fundamentals of Mechanics - CIVE 1140

Kinetics Examples

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Section 1: Velocity and acceleration

    1. A swimmer swims at a steady 1m/s across a lake and then swims back at a steady speed of 0.5m/s. What is the swimmers average speed?

      2. (2/3 m/s)
    2. A car travelling at 50 km/h stops in 11m. Find its deceleration (assuming it is uniform.)

      3. (8.87 m/s2)
    3. A wagon starts to run, from rest, down an incline. In 30 s it travels 100m. How long would it take to travel 800m from rest?

      4. (8.48 s)
    4. A stone is dropped down a vertical shaft 200m deep. The speed of sound in air is 330 m/s. Find the time that elapses before the person dropping the stone hears it hit the bottom.

      5. (6.986 s)
    5. A lift starts from rest and accelerates at 2m/s2 until it reaches a speed of 3m/s. It then travels at constant speed until it is finally brought to rest with a deceleration of 1m/s2. The total time of motion is 20s. Sketch the speed / time graph and find the total distance travelled.

      6. (53.25 m)
    6. A crane lifts a load of 900kg vertically with constant acceleration from rest. The load rises 10m in 5s. Find the acceleration of the load and the tension in the lifting cable.

      7. (0.8 m/s2, 9.54 kN)
    7. A hoist raises material from the ground to the top of a building 100m high. It accelerates at 1m/s2 for 1s and decelerates at 0.8m/s2. Sketch the speed / time graph and find the uniform speed and the total time of travel from the ground to the top of the building.

      8. (1 m/s, 101.125 s)
    8. A train accelerates and decelerates at 0.5m/s2. What is the minimum time it can take to travel between two stations 5km apart?

      9. (200 s)
    9. A man gets out of a train and walks along the platform at 2m/s. the train begins to move 30s later and accelerates at 0.5m/s2. How much further time will elapse before the door from which the man left the train overtakes him?

      10. (20 s)
    10. A pulley with diameter 1m rotates 120 times per minute. It has a belt passing round it. What is the angular speed of the pulley? What is the linear speed of the belt?

      11. (12.57 rad/s, 6.28 m/s)
    11. Find the linear speed of a point on the earth's equator assuming that the radius of the earth is 6380km

      12. (464 m/s)
    12. A flywheel rotates at 300 rev/min. It slows down uniformly to 180 rev/min in 30s. What is its angular acceleration?

      13. (-0.42 rad/s2)
    13. A grinding wheel is accelerated uniformly from rest to 3000 rev/min in 3.0s. Find its angular acceleration. If the wheel diameter is 200mm, find the final linear speed of a point on its rim.

      14. (104 rad/s2, 31.4 m/s)
    14. A train on a level straight track accelerates uniformly from rest to 60 km/h in a distance of 300m. Find its acceleration. If the driving wheels are 1.5m diameter, find their angular acceleration and the final angular speed of a point on the rim of the wheel.

      15. (0.463 m/s2, 0.617 rad/s2, 22.2 rad/s)