Resultant forces

A student measures the length of a spring when it is horizontal and when it is vertical, as shown in Figures 9a and 9b.

The length, Y, of the vertical spring in Figure 9b is greater than the length, X, of the horizontal spring in Figure 9a.

Give a reason why the length of the spring in Figure 9b is greater than the length of the the spring in Figure 9a.

The student adds some weights to the end of the spring, as shown in Figure 10b.

(Source: https://www.shalom-education.com/courses/ks3-physics/lessons/motion-and-forces/topic/deformation-and-hookes-law/)

The extension of the spring due to these added weights is equal to

The extension of the spring in Figure 10b is now determined for different weights added to the spring up to a maximum of 6 N.

Figure 11 shows a graph of the results.

The increase in potential energy stored in the spring is equal to the area under the graph in Figure 11.

Calculate the increase in potential energy stored in the spring when the spring is extended from 0 cm to 8 cm.

Give your answer in joules (J).

Calculate the spring constant of the spring using data from the graph in Figure 11.

State the unit.

spring constant =_........ unit_........

The box in Figure 12 represents a weight added to the end of the spring.

Figure 12

Draw two vectors on Figure 12 to complete a free body force diagram of a 5 N weight in equilibrium.

Figure 13 shows two forces, P and Q, acting at point X.

Complete the diagram in Figure 13 to show the size and direction of the resultant force, R, on point X.

Figure 3 shows two magnets with their N poles facing each other.

Figure 3

On Figure 3, draw the shape and direction of the magnetic field between the two magnets.

Figure 4 shows a toy that has a plastic cylinder, a plastic base and two similar magnets. Each of the two magnets is in the shape of a ring.

The upper magnet seems to float in the air above the lower magnet.

Describe the forces acting on the upper magnet.

Use the idea of magnetic fields in your answer.

Figure 5 shows a current‑carrying wire between the poles of a magnet.

The magnet and the wire each experience a force when there is a current in the wire.

1 State the direction of the force on the wire.

2 State the direction of the force on the magnet.

The force on the wire is 0.15 N.

The current in the wire is 2.7 A.

The magnet produces a field with a magnetic flux density of 0.50 T.

Calculate the length of the wire in the magnetic field.

Use an equation selected from the list of equations given at the end of the question paper.

length of the wire in the magnetic field =_........ m

Figure 6 shows part of the inside of a pen.

The pen contains a spring that can be compressed.

The spring constant of the spring is 260 N/m.

Calculate the force needed to compress the spring by the amount shown in Figure 6.

Give your answer to an appropriate number of significant figures.

force =_........ N

A student removes the spring from the pen and investigates the compression of the spring.

Figure 7 shows the equipment and the procedure that the student uses.

ruler fixed in place above the electronic balance

The student presses down on the spring to change its length.

The electronic balance measures the force applied to the spring.

Describe how the student can determine the change in length of the spring. You may add to Figure 7 to help your answer.

The student finds it difficult to make an accurate measurement of the change in length of the spring using the equipment as shown.

Describe one way that the student could improve the procedure.

Figure 8 shows a different spring hanging from a hook fixed to the ceiling.

A block hangs from the other end of the spring.

The weight of the spring is 1 N. The weight of the block is 5 N.

The force exerted on the top of the spring by the hook is

Figure 9 shows two forces, P and Q, acting at point X.

Complete the diagram in Figure 9 to show the size and direction of the resultant force, R, on point X.

The magnitude and direction of a force can be represented by a vector. Figure 13 shows the forces acting on four identical trolleys. The arrows show the magnitude and direction of the forces.

Which diagram shows a pair of forces that will produce zero acceleration?

Figure 14 shows two small boats pulling a much larger ship.

The ship is connected to the boats with ropes.

The tension, T, in each of the ropes has a magnitude of 20 kN.

The ropes are at right angles to each other.

Draw a vector diagram and use it to determine the resultant force that the boats exert on the ship.

magnitude of resultant force on the ship =_........ kN

*(c) Figure 15 shows a wooden block connected to a weight by a string. The string goes over a pulley.

The surfaces of the table and the wooden block are both rough.

wooden block

The wooden block moves across the table at a constant horizontal velocity.

Several vertical and horizontal forces act on the wooden block as it moves.

Explain how the forces keep the wooden block moving across the table at a constant horizontal velocity.

Your answer should refer to all forces acting on the wooden block.

You may add to the diagram to help with your answer.

Figure 5 shows the vertical forces on an aeroplane.

Use information from the diagram to determine the size and direction of the resultant vertical force on the aeroplane.

size =_........ kN, direction is_........

The aeroplane is descending.

Figure 6 shows a diagram of the resultant vertical and horizontal forces on the aeroplane as it is descending.

Complete the diagram to show the resultant of these two forces.

The mass of the aeroplane is 750 kg.

Calculate the change in gravitational potential energy of the aeroplane as it descends from 1300 m to the ground.

Gravitational field strength (g) = 10 N/kg

energy =_........ J

The aeroplane is powered by an engine that burns fuel.

The fuel supplies a total of 6500 kJ of energy every minute.

The efficiency of the engine is 0.70 (70%).

Calculate the power output of the engine.

Give your answer in kW.

power =_........ kW

Explain why the efficiency of the engine is less than 1 (100%).