Resultant forces

Very long trains can be pulled by more than one engine.

A train is made up of four engines pulling trucks filled with coal.

The coal in one truck has a mass of 75 000 kg.

gravitational field strength = 9.8 N/kg

Calculate the weight of the coal in one truck.

Use the equation:

weight = mass × gravitational field strength

One engine exerts a forward force of 850 000 N.

Calculate the work done by one engine when the train moves a distance of 80 m.

Use the equation:

work done = force × distance moved

Each of the four engines exerts a forward force of 850 000 N on the trucks.

Calculate the total forward force on the trucks.

The force exerted by the engines on the trucks is a contact force.

Which of the following is also a contact force?

Tick (✓) one box.

Which sketch graph represents the train moving at a constant speed?

Tick (✓) one box.

The train accelerates for 150 s.

The velocity of the train changes from 16 m/s to 25 m/s.

Calculate the acceleration of the train.

Use the equation:

In a world record attempt, a skydiver jumped from a height of 40 km above the Earth.

Figure 6 shows an incomplete free-body diagram for the skydiver a few seconds after the start of the jump.

Figure 6

The skydiver has not reached terminal velocity.

Complete the free-body diagram in Figure 6.

During the first 2.5 minutes the mean acceleration of the skydiver was 0.64 m/s².

The initial velocity of the skydiver was 0 m/s.

Calculate the velocity of the skydiver 2.5 minutes after the start of the jump.

Use the Physics Equations Sheet.

The skydiver accelerated until reaching terminal velocity.

Explain why the skydiver reached terminal velocity.

Explain why the atmospheric pressure acting on the skydiver increased as the skydiver fell.

The skydiver opened his parachute.

A few seconds after opening the parachute, the resultant vertical force on the skydiver was 240 N upwards.

The wind caused a resultant horizontal force of 200 N to the left on the skydiver.

Draw a vector diagram to determine the resultant force on the skydiver.

Figure 17 shows a young child using a baby walker.

The child is standing still.

What is the resultant vertical force on the child?

Give a reason for your answer.

Use the Physics Equations Sheet to answer questions 09.2 and 09.3.

Write down the equation which links distance (s), force (F) and work done (W).

The child pushed the baby walker 2.8 m across a horizontal floor.

The work done by the child was 35 J.

Calculate the horizontal force the child applied to the baby walker.

The child pushed the baby walker from a carpet onto a hard floor.

The child applied the same horizontal force to the baby walker.

Explain why the speed of the baby walker increased.

There are some toy gears on the front of the baby walker.

Figure 18 shows the gears.

The child applies a force to gear A.

This causes a moment about the pivot, so gear A rotates.

Use the Physics Equations Sheet to answer questions 09.5 and 09.6.

Write down the equation which links distance (d), force (F) and moment of a force (M).

The child applies a force of 2.0 N on gear A.

The perpendicular distance between the force and the pivot is 7.5 cm.

Calculate the moment of the force about the pivot.

Explain what happens to gear B when the child applies the force to gear A.

Figure 5 shows a young child using a baby walker.

The child is standing still.

What is the resultant vertical force on the child?

Give a reason for your answer.

Use the Physics Equations Sheet to answer questions 02.2 and 02.3.

Write down the equation which links distance (s), force (F) and work done (W).

The child pushed the baby walker 2.8 m across a horizontal floor.

The work done by the child was 35 J.

Calculate the horizontal force the child applied to the baby walker.

The child pushed the baby walker from a carpet onto a hard floor.

The child applied the same horizontal force to the baby walker.

Explain why the speed of the baby walker increased.

There are some toy gears on the front of the baby walker.

Figure 6 shows the gears.

The child applies a force to gear A.

This causes a moment about the pivot, so gear A rotates.

Use the Physics Equations Sheet to answer questions 02.5 and 02.6.

Write down the equation which links distance (d), force (F) and moment of a force (M).

The child applies a force of 2.0 N on gear A.

The perpendicular distance between the force and the pivot is 7.5 cm.

Calculate the moment of the force about the pivot.

Explain what happens to gear B when the child applies the force to gear A.

Figure 25 shows the route an aeroplane takes as it travels from an airport terminal to the runway. Figure 25 has been drawn to scale.

Determine the magnitude of the aeroplane’s displacement from the start point to the finish point on Figure 25.

Figure 26 shows the direction of the horizontal forces acting on the aeroplane as it moves in a straight line towards the runway.

Determine the magnitude of the resultant horizontal force on the aeroplane.

Describe the motion of the aeroplane as it moves towards the runway.

Air resistance and friction are contact forces. Give one other example of a contact force.

The aeroplane stops for a short time and then accelerates along the runway. Figure 27 shows a distance–time sketch-graph for this stage of the journey.

Draw the velocity–time sketch-graph for this stage of the journey on Figure 28.

The aeroplane takes off from the runway, so its height above the ground increases. Figure 29 shows how atmospheric pressure varies with the height of the aeroplane above the ground.

Estimate the atmospheric pressure when the height of the aeroplane above the ground is 10 km.

What happens to the air surrounding the aeroplane as the height of the aeroplane above the ground increases? Tick (✓) one box.

Figure 3 shows the route an aeroplane takes as it travels from an airport terminal to the runway. Figure 3 has been drawn to scale.

Determine the magnitude of the aeroplane’s displacement from the start point to the finish point on Figure 3.

Figure 4 shows the direction of the horizontal forces acting on the aeroplane as it moves in a straight line towards the runway.

Determine the magnitude of the resultant horizontal force on the aeroplane.

Describe the motion of the aeroplane as it moves towards the runway.

Air resistance and friction are contact forces. Give one other example of a contact force.

The aeroplane stops for a short time and then accelerates along the runway. Figure 5 shows a distance–time sketch-graph for this stage of the journey.

Draw the velocity–time sketch-graph for this stage of the journey on Figure 6.

The aeroplane takes off from the runway, so its height above the ground increases. Figure 7 shows how atmospheric pressure varies with the height of the aeroplane above the ground.

Estimate the atmospheric pressure when the height of the aeroplane above the ground is 10 km.

What happens to the air surrounding the aeroplane as the height of the aeroplane above the ground increases? Tick (✓) one box.

Hailstones are small balls of ice. Hailstones form in clouds and fall to the ground.

Figure 3 shows different-sized hailstones.

Which force causes the hailstones to fall to the ground?

Tick (✓) one box.

As the hailstones begin to fall they accelerate.

Which force increases as the hailstones accelerate?

Tick (✓) one box.

After a short time hailstones fall at terminal velocity.

Which of the following statements is true at terminal velocity?

Tick (✓) one box.

A scientist investigated how the terminal velocity of hailstones varies with their diameter.

Figure 4 shows the results.

Estimate the terminal velocity for a hailstone with a diameter of 80 mm.

Show how you obtain your answer.

Give one reason why a hailstone with a large diameter has a greater terminal velocity than a hailstone with a smaller diameter.

Tick (✓) one box.

After falling, the hailstone hits the ground.

Figure 5 shows the forces acting on the hailstone at the moment it hits the ground.

What is the magnitude of the resultant force on the hailstone in Figure 5 ?

Tick (✓) one box.

What is the direction of the resultant force on the hailstone in Figure 5 ?

Diving bricks sink to the bottom of a swimming pool.

Figure 14 shows a diving brick.

Swimmers practise diving to the bottom of the swimming pool to pick up the diving brick.

Explain why the forces on the brick at the bottom of the pool cause the brick to be stationary.

When the brick from Figure 14 is at the bottom of the pool, the top surface of the brick is 2.50 m below the surface of the water.

The force acting on the top surface of the brick due to the weight of the water is 637 N.

gravitational field strength = 9.8 N/kg

Calculate the density of the water in the swimming pool.

Use the Physics Equations Sheet.

Professional divers are trained in a very deep swimming pool.

The density of the water in this pool is not the same as the density of the water in Question 08.2

The diving brick was dropped into the very deep swimming pool.

When the brick was at a depth of 2.50 m, the force due to the weight of the water on the top surface of the brick was 618 N.

Figure 15 shows the diving brick at the bottom of the very deep swimming pool.

Determine the force due to the weight of the water on the top surface of the brick in Figure 15.

Use the Physics Equations Sheet.

Give your answer to 3 significant figures.

Figure 11 shows a cyclist riding a bicycle. Force A causes the bicycle to accelerate forwards.

What name is given to force A ?

Figure 12 shows how the velocity of the cyclist changes during a short journey.

Determine the distance travelled by the cyclist between Y and Z.

Figure 13 shows the gears on the bicycle.

Describe how the force on the pedal causes a moment about the rear axle.

Figure 14 shows a different cyclist towing a trailer.

The speed of the cyclist and trailer increased uniformly from 0 m/s to 2.4 m/s. The cyclist travelled 0.018 km while accelerating. Calculate the initial acceleration of the cyclist.

The resultant force of the towbar on the trailer has a horizontal component and a vertical component. horizontal force = 200 N vertical force = 75 N

Determine the magnitude and direction of the resultant force of the towbar on the trailer by drawing a vector diagram.

An aeroplane is 4000 m above the Earth’s surface. A skydiver jumps from the aeroplane and falls vertically. Figure 15 shows the distance the skydiver falls during the first 12 seconds after jumping.

Figure 16 shows part of the free body diagram for the skydiver three seconds after jumping. Complete the free body diagram for the skydiver.

Explain the changing motion of the skydiver in terms of the forces acting on the skydiver.

Use Figure 15 to determine the speed of the skydiver between 7 seconds and 12 seconds.

In 2012 a skydiver jumped from a helium balloon 39 000 metres above the Earth’s surface. The skydiver reached a maximum speed of 377 m/s Jumping from 39 000 metres allowed the skydiver to reach a much higher speed than a skydiver jumping from 4000 metres. Explain why.

Figure 7 shows four blocks of different materials floating on water. The four blocks are the same volume.

Which of the blocks has the smallest weight? Tick one box.

Figure 8 shows a lifebuoy next to a deep swimming pool.

The lifebuoy has a mass of 2.5 kg. gravitational field strength = 9.8 N/kg Calculate the weight of the lifebuoy. Use the equation: weight = mass × gravitational field strength

When thrown into the water the lifebuoy floats. The two forces acting on the lifebuoy are the weight of the lifebuoy downwards and upthrust upwards. How big is the upthrust on the lifebuoy compared to the weight of the lifebuoy? Tick one box.

Write down the equation which links acceleration, mass and resultant force.

A rope is used to pull the lifebuoy to the side of the swimming pool. A resultant force of 4.0 N acts on the lifebuoy. The mass of the lifebuoy is 2.5 kg. Calculate the acceleration of the lifebuoy.

Figure 8 shows a boat floating on the sea. The boat is stationary.

Figure 9 shows part of the free body diagram for the boat. Complete the free body diagram for the boat.

Figure 9

Calculate the mass of the boat. Use the information given in Figure 9. gravitational field strength = 9.8 N/kg Give your answer to two significant figures.

When the boat propeller pushes water backwards, the boat moves forwards. The force on the water causes an equal and opposite force to act on the boat. Which law is this an example of?

Figure 10 shows the boat towing a small dinghy.

Figure 10

The tension force in the tow rope causes a horizontal force forwards and a vertical force upwards on the dinghy. horizontal force forwards = 150 N vertical force upwards = 50 N

Figure 11 shows a grid. Draw a vector diagram to determine the magnitude of the tension force in the tow rope and the direction of the force this causes on the dinghy.

Figure 11

Direction of the force on the dinghy caused