Name……………………

Class……………..

IB Physics Topic 2. Mechanics

STUDENT WORKBOOK

Questions Worksheet #1 – Motion ( /39)

1. (a) Circle all the scalar quantities in the list below. [1]

density speed weight velocity volume acceleration

(b) The distance between the Sun and the Earth is 1.5 × 1011 m. Calculate the time in minutes for light to travel

from the Sun to the Earth. The speed of light is 3.0 × 108 m s–1.

time = .............................. min [2]

(c) The terminal velocity of a raindrop falling vertically through air is 4.0 m s–1.

(i) In terms of the forces acting on the raindrop, explain why it is at terminal velocity.

..................................................................................................................................................................................

..................................................................................................................................................................................

............................................................................................................................................................................ [2]

(ii) Fig. 1.2 shows a velocity vector diagram for the falling raindrop in a horizontal crosswind of speed 1.5 m s–1.

1. On Fig. 1.2, draw an arrow on the raindrop to show the direction in which it will travel.

2. Calculate the magnitude of the resultant velocity of the raindrop. Use the space below for your working.

resultant velocity = .................................. m s–1 [3] [Total: 8]

2. Fig. 2.1 shows an arrangement used in the laboratory to determine the acceleration g of free fall.

The steel ball is held at rest by an electromagnet. When the electromagnet is switched off, the electronic timer is started and the ball falls. The timer is stopped when the ball opens the trapdoor. The distance between the bottom of the ball and the top of the trapdoor is 0.600 m. The timer records a time of fall of 0.356 s. (i) Show that the value for the acceleration g of free fall obtained from this experiment is 9.47 m s–2.

[2] (ii) State one reason why the experimental value in (i) is less than 9.81 m s–2.

..................................................................................................................................................................................

..................................................................................................................................................................................

........................................................................................................................................................................... [1]

Continued on next page

(iii) On Fig. 2.2 sketch a graph to show the variation of the vertical distance s fallen by the ball with time t. [1]

[Total: 4]

3. (a) Define braking distance of a car. ..................................................................................................................................................................................

..................................................................................................................................................................................

........................................................................................................................................................................... [1]

(b) Other than the speed of the car, state two factors that affect the braking distance of a car. Describe how the braking distance is affected by each factor. 1. ..............................................................................................................................................................................

..................................................................................................................................................................................

..................................................................................................................................................................................

..................................................................................................................................................................................

2. ..............................................................................................................................................................................

..................................................................................................................................................................................

..................................................................................................................................................................................

............................................................................................................................................................................. [4]

(c) Fig. 5.1 shows the variation of braking distance with speed v of a car.

(i) The car is travelling on a level straight road at a speed of 20 m s–1. The reaction time of the driver is 0.50 s. 1. Calculate the thinking distance.

thinking distance = ........................................... m 2. Hence, determine the stopping distance of the car.

stopping distance = .......................................... m [3]

(ii) In Fig. 5.1, the braking distance is directly proportional to the square of the speed. Determine the braking distance of the car when travelling at a speed of 32 m s–1.

braking distance = .................................. m [2] [Total: 10]

3. A student has been asked to determine the linear acceleration of a toy car as it moves down a slope. He sets up the apparatus as shown in Fig. 3.1.

The time t to move from rest through a distance d is found for different values of d. A graph of d (y-axis) is plotted against t2 (x-axis) as shown in Fig. 3.2.

Continued on next page

(a) Theory suggests that the graph is a straight line through the origin. Name the feature on Fig. 3.2 that indicates the presence of:

(i) random error,

...................................................................................................................................................................................

(ii) systematic error.

..............................................................................................................................................................................[2]

(b)(i) Determine the gradient of the line of the graph in Fig. 3.2.

gradient = ........................................... [2]

(ii) Use your answer to (i) to calculate the acceleration of the toy down the slope. Explain your working.

acceleration = ................................... m s–2 [3] [Total: 7]

4. (a) A stone of mass 56 g is thrown horizontally from the top of a cliff with a speed of 18 m s–1, as illustrated in Fig. 4.1.

The initial height of the stone above the level of the sea is 16 m. Air resistance may be neglected. (i) Calculate the change in gravitational potential energy of the stone as a result of falling through 16 m.

change = ....................................... J [2] (ii) Calculate the total kinetic energy of the stone as it reaches the sea.

kinetic energy = ...................................... J [3]

(b) Use your answer in (a)(ii) to show that the speed of the stone as it hits the water is approximately 25 m s–1.

[1] (c) State the horizontal velocity of the stone as it hits the water.

horizontal velocity = ..................................... m s–1 [1]

(d) (i) On the grid of Fig. 4.2, draw a vector diagram to represent the horizontal velocity and the resultant velocity of the stone as it hits the water. [1]

(ii) Use your vector diagram to determine the angle with the horizontal at which the stone hits the water.

angle = ............................................ ° [2] [Total: 10]

Questions Worksheet #2 – Forces ( /31)

1. (a) Define the newton.

..................................................................................................................................................................................

........................................................................................................................................................................... [1]

(b) Fig. 3.1 shows a spaceship on the surface of the Earth.

The mass of the spaceship is 1.9 × 106 kg. During lift off, the spaceship rockets produce a vertical upward force

of 3.1 × 107 N.

(i) Calculate the weight of the spaceship.

weight = ...................................... N [1]

(ii) Calculate the initial vertical acceleration as the spaceship lifts off.

acceleration = ................................ m s–2 [2]

(iii) The vertical upward force on the spaceship stays constant. Explain why the acceleration of the spaceship

increases after liftoff.

..................................................................................................................................................................................

..................................................................................................................................................................................

..................................................................................................................................................................................

.......................................................................................................................................................................... [1]

[Total: 5]

2. This question is about estimating the pressure exerted by a person wearing shoes standing on a floor, see

Fig. 1.1.

(i) Estimate the weight in newtons of a person.

weight = ...................................................... N [1]

(ii) Estimate the total area of contact in square metres between the shoes of this person and the floor.

area = ................................................... m2 [1]

(iii) Hence estimate the pressure in pascals exerted by this person standing on the floor.

pressure = .................................................. Pa [1] [Total: 3]

3. The force against length graph for a spring is shown in Fig. 6.1.

(a) Explain why the graph does not pass through the origin. ..................................................................................................................................................................................

............................................................................................................................................................................ [1]

(b) State what feature of the graph shows that the spring obeys Hooke’s law.

..................................................................................................................................................................................

............................................................................................................................................................................ [1]

(c) The gradient of the graph is equal to the force constant k of the spring. Determine the force constant of the spring.

force constant = ............................. N m–1 [2]

[Total: 4]

4. A lift has a mass of 500 kg. It is designed to carry a maximum of 8 people of total mass 560 kg. The lift is supported by a steel cable of cross-sectional area 3.8 × 10–4 m2. When the lift is at ground floor level the cable is at its maximum length of 140 m, as shown in Fig. 3.1. The mass per unit length of the cable is 3.0 kg m–1.

(a) Show that the mass of the 140 m long steel cable is 420 kg.

[1]

(b) The lift with its 8 passengers is stationary at the ground floor level. The initial upward acceleration of the lift and the cable is 1.8 m s–2. Show that the maximum tension in the cable at point P is 1.7 × 104 N.

[4] [Total: 5]

5. Fig. 4.1 shows a ship S being pulled by two tug-boats.

The ship is travelling at a constant velocity. The tensions in the cables and the angles made by these cables to the direction in which the ship travels are shown in Fig. 4.2. (i) Draw a vector triangle and determine the resultant force provided by the two cables.

resultant force = ................................. kN [3] (ii) State the value of the drag force acting on the ship S. Explain your answer. ..................................................................................................................................................................................

..................................................................................................................................................................................

............................................................................................................................................................................ [2]

[Total: 5]

6. Fig. 2.1 shows two masses A and B tied to the ends of a length of string. The string passes over a pulley. The mass A is held at rest on the floor.

The mass A is 1.20 kg and the mass B is 1.50 kg. (a) Calculate the weight of mass B.

weight = .............................................. N [1] (b) Mass B is initially at rest at a height of 2.80 m above the floor. Mass A is then released. Mass B has a constant downward acceleration of 1.09 m s–2. Assume that air resistance and the friction between the pulley and the string are negligible. (i) In terms of forces, explain why the acceleration of the mass B is less than the acceleration of free fall g. ..................................................................................................................................................................................

............................................................................................................................................................................. [1]

(ii) Calculate the time taken for the mass B to fall 1.40 m.

time = .......................................... s [3]

(iii) Calculate the velocity of mass B after falling 1.40 m.

velocity = ..................................... m s–1 [2]

(iv) Mass B hits the floor at a speed of 2.47 m s–1. It rebounds with a speed of 1.50 m s–1. The time of contact with the floor is 3.0 × 10–2 s. Calculate the magnitude of the average acceleration of mass B during its impact with the floor.

acceleration = ................................... m s–2 [2] [Total: 9]

Questions Worksheet #3 – Energy, Work and Power ( /31)

(a) State the principle of conservation of energy. ..................................................................................................................................................................................

............................................................................................................................................................................ [1]

(b) Describe one example where elastic potential energy is stored.

.................................................................................................................................................................................

.............................................................................................................................................................................. [1]

(c) Fig. 5.1 shows a simple pendulum with a metal ball attached to the end of a string.

When the ball is released from P, it describes a circular path. The ball has a maximum speed v at the bottom of its swing. The vertical distance between P and bottom of the swing is h. The mass of the ball is m. (i) Write the equations for the change in gravitational potential energy, Ep, of the ball as it drops through the height h and for the kinetic energy, Ek, of the ball at the bottom of its swing when travelling at speed v. Ep = Ek = [1] (ii) Use the principle of conservation of energy to derive an equation for the speed v. Assume that there are no energy losses due to air resistance.

[2] [Total: 5]

2. (a) Define work done by a force. ..................................................................................................................................................................................

............................................................................................................................................................................ [2]

(b) Define power. ...................................................................................................................................................................................

............................................................................................................................................................................. [1]

(c) Explain why the efficiency of a mechanical device can never be 100%. ..................................................................................................................................................................................

............................................................................................................................................................................ [1]

(d) A car has a total mass of 810 kg. Its speed changes from zero to 30 m s–1 in a time of 12 s. (i) Calculate the change in the kinetic energy of the car.

change in kinetic energy = .................................... J [2] (ii) Calculate the average power generated by the car engine. Assume that the power generated by the engine of the car is entirely used in increasing the kinetic energy of the car.

power = ......................................................W [1] (iii) The actual efficiency of the car is 25%. The car takes 18 kg of petrol to fill its tank. The energy provided per kilogram of petrol is 46 MJ kg–1. The drag force acting on the car at a constant speed of 30 m s–1 is 500 N. 1. Calculate the work done against the drag force per second.

work done per second = .............................. J s–1 [1] 2. Calculate the total distance the car can travel on a full tank of petrol when travelling at a constant speed of 30 m s–1.

distance = ............................................ m [3] [Total: 11]

3. Fig. 11.1 shows a children’s ride. A carriage containing children is pulled up the slope by a motor. The carriage stops at A and then runs down through B, C and D without further input of energy. Between D and E the carriage turns through a bend at constant speed, as shown in Fig. 11.2. At E, brakes are applied and the carriage slows to a stop at F. The height of the ride is 30 m at A and 10 m at C.

The mass of the carriage and children is 500 kg.

Take the gravitational field strength as 10 N/kg.

(a) (i) Discuss the energy changes that occur in the ride from A to D.

……………………………………………………………………………………………………………………………………………………………………………

……………………………………………………………………………………………………………………………………………………………………………

…………………………………………………………………………………………………………………………………………………………………….. [3]

(ii) Calculate the maximum potential energy of the carriage and children.

……………………………………………………………………………………………………………………………………………………………………………

……………………………………………………………………………………………………………………………………………………………………………

[3]

Continued on next page

(iii) Assuming that there is no friction between A and C, determine the kinetic energy of the carriage and

children at C. Show your working.

[3]

(b) Between D and E, the carriage goes round part of a horizontal circle at constant speed.

During this time the velocity of the carriage changes. (i) Explain how the carriage can have a constant speed but a changing velocity. ……………………………………………………………………………………………………………………………………………………………………………

……………………………………………………………………………………………………………………………………………………………………… [2]

(ii) State the direction of the force that acts on the carriage to make it move round the curve. …………………………………………………………………………………………………………………………………………………………………….. [1]

(c) Between E and F, a frictional force of 3000 N acts to slow the carriage. Calculate the deceleration of the carriage.

[3] [Total: 15]

Questions Worksheet #4 – Momentum ( /27)

1. (a) (i) State the principle of conservation of linear momentum. ..................................................................................................................................................................................

..................................................................................................................................................................................

........................................................................................................................................................................... [2]

(ii) Explain what is meant by an inelastic collision. ..................................................................................................................................................................................

........................................................................................................................................................................... [1]

(iii) Fig. 1.1 shows the head-on-collision of two blocks on a frictionless surface.

Before the collision, the 2.4 kg block is moving to the right with a speed of 3.0 m s–1 and the 1.2 kg block is moving to the left at a speed of 2.0 m s–1. During the collision the blocks stick together. Immediately after the collision the blocks have a common speed v. 1. Calculate the speed v.

v = .................................... m s–1 [2] 2. Show that this collision is inelastic.

[2] [Total: 7]

2. A ball B of mass 1.2 kg travelling at constant velocity collides head-on with a stationary ball S of mass 3.6 kg, as shown in Fig. 2.1.

Frictional forces are negligible. The variation with time t of the velocity v of ball B before, during and after colliding with ball S is shown in Fig. 2.2.

(a) State the significance of positive and negative values for v in Fig. 2.2. ..................................................................................................................................................................................

............................................................................................................................................................................. [1]

(b) Use Fig. 2.2 to determine, for ball B during the collision with ball S,

(i) the change in momentum of ball B,

change in momentum = ................................. N s [3]

(ii) the magnitude of the force acting on ball B.

force = ....................................... N [3]

(c) Calculate the speed of ball S after the collision.

speed = ....................................... m s–1 [2]

(d) Using your answer in (c) and information from Fig. 2.2, deduce quantitatively whether the collision is elastic or inelastic.

..................................................................................................................................................................................

............................................................................................................................................................................ [2]

[Total: 11]

3. A bullet of mass 2.0 g is fired horizontally into a block of wood of mass 600 g. The block is suspended from strings so that it is free to move in a vertical plane. The bullet buries itself in the block. The block and bullet rise together through a vertical distance of 8.6 cm, as shown in Fig. 3.1.

(a)(i) Calculate the change in gravitational potential energy of the block and bullet.

change = ......................................... J [2] (ii) Show that the initial speed of the block and the bullet, after they began to move off together, was 1.3 m s-1.

[1]

(b) Using the information in (a)(ii) and the principle of conservation of momentum, determine the speed of the bullet before the impact with the block.

speed = ................................. m s–1 [2]

(c) (i) Calculate the kinetic energy of the bullet just before impact.

kinetic energy = ....................................... J [2] (ii) State and explain what can be deduced from your answers to (c)(i) and (a)(i) about the type of collision between the bullet and the block. ...................................................................................................................................................................................

...................................................................................................................................................................................

.............................................................................................................................................................................. [2]

[Total: 9]