Year 11 Physics Vectors Sheet 1

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This is a sheet of harder questions on vectors.

  1. A river flows at 3.0 km/h. The river is 100.0 m wide and a boat is to arrive on the opposite bank 80.0 m downstream from its starting point. What is the velocity of the boat relative to the water if the time of crossing is 5.0 minutes? [2.4km/h at 31° to the upstream bank]
  2. A river 1.0 km wide flows due north at 8.0 km/h. A motor launch travels at 6.0 km/h relative to the water. A person starts from the west bank and wishes to reach the point directly opposte on the east bank. If the person can walk at 3.0 km/h find the direction in which the motor launch should head so that the person can make the journey in the minimum time.[E33°S]
  3. Relative to a cyclist travelling to the west at 40km/h the wind appears to be coming from the south. On doubling their speed the wind appears to be coming from the south-west. What is the velocity of the wind?[56.6km/h NW]
  4. A cyclist travelling on a straight road at 10 km/h is subject to air resistance proportional to the square of their speed. By what factor must they increase their power output to maintain their speed if a 20 km/h cross wind develops?[51/2]
  5. An ocean liner is travelling in a straight line at a speed of 20km/h that takes it 1.0 km from a port. A boat that can travel at 12km/h is to leave the port at the last possible time and move in a straight line to meet the ocean liner. What is the distance travelled by the boat when it reaches the liner? [1.25km]

IB Physics Mass and Spring

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A tutorial sheet of questions on a mass and a spring is given below.

  1. Two springs each of force constant k are connected in series and held vertically. A mass M is placed on the lower end of the combination. What is the extension produced?
  2. A mass M rests on a smooth horizontal surface. Identical springs of force constant k are attached to opposite sides of the mass. The other ends of the springs are held at rest. What is the period of oscillation of the mass when it is released after being displaced (a) along the line of the springs, (b) perpendicular to the line of the springs.
  3. A spring of force constant k is held vertically with its upper end fixed. A mass M is placed on the lower end of the spring. The mass is then pulled down a distance A and released from rest. (a) Explain why the period of oscillation does not depend on g. (b) Does the period of oscillation does depend on A? (c) Instead of being released from rest the mass is given an initial velocity u downwards at the pulled down position. What is the period of the oscillation in this case?
  4. Does a mass oscillating on a spring in a vertical plane have gravitational potential energy?
  5. A light spring is hanging loosely from the ceiling. A mass is placed on the free end of the spring and released from rest. The mass moves downwards a distance of 40 cm before starting to rise again. What is the period of the simple harmonic motion?[0.90s]
  6. A block of mass M is connected to a light spring of force constant k. The block is placed on a smooth inclined plane of angle of elevation 𝜽. The other end of the spring is held at rest with the spring parallel to the inclined plane. The mass is set moving in simple harmonic motion. Does the period of oscillation depend on 𝜽?
  7. A block of mass M slides a distance d from rest down a smooth inclined plane making an angle 𝜽 with the horizontal. It hits a light spring of natural length L and force constant k at the bottom of the incline. Determine the amount that the spring is compressed when the block comes to rest.
  8. A bungee jumper of mass M is attached to an elastic cord of unstretched length L and force constant k. If they jump from rest how far do they fall before they come to rest?