Resultant forces

A student measures the length of a spring when it is horizontal and when it is vertical, as shown in Figures 15a and 15b.

The length, Y, of the vertical spring in Figure 15b is greater than the length, X, of the spring in Figure 15a.

Give a reason why the length of the spring in Figure 15b is greater than the length of the spring in Figure 15a.

The student adds some weights to the end of the spring, as shown in Figure 16b.

(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 16b is now determined for different weights added to the spring up to a maximum of 6 N.

Figure 17 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 17.

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 17.

State the unit.

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

The box in Figure 18 represents a weight added to the end of the spring.

Figure 18

Draw two vectors on Figure 18 to complete a free body force diagram of a 5 N weight in equilibrium.

Figure 19 shows two forces, P and Q, acting at point X.

Complete the diagram in Figure 19 to show the size and direction of the resultant force, R, on point X.

Figure 16 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 16.

Give your answer to an appropriate number of significant figures.

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

Figure 17 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 17 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 18 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 19 shows two forces, P and Q, acting at point X.

Complete the diagram in Figure 19 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 22 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 23 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.

*(c) Figure 24 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 17 shows a crane lifting a concrete block from the bottom of a deep pool of water. The top of the block is a distance, h, below the surface of the water.

The force on the top of the block due to the water above it is 41 000 N.

The pressure due to the water on the top surface of the block is 66 000 Pa.

Calculate the area of the top surface of the block.

The density of water is 1000 kg/m³.

Calculate the distance, h, between the top of the block and the surface of the water.

Gravitational field strength, g, is 10 N/kg.

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

Explain why there is an upthrust produced by the water on the block.

*(iv) The crane raises the block until it is high enough out of the water to be loaded on to a lorry.

The block moves upwards at a constant speed even though the lifting force in the cable changes.

Figure 18 shows the graph of how the lifting force changes while the block is being raised.

Explain why the lifting force changes as shown on the graph in Figure 18. Include calculation(s) in your answer.

Figure 14 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.

The aeroplane is descending.

Figure 15 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

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.

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