Forces (Cambridge O Level Physics)

A student stretches a spring by adding different loads to it. She measures the length of the spring for each load. She plots a graph of the results.

Fig. 2.1 shows the graph of her results.

Use the graph to determine:

Complete the sentence about effects of forces. Choose words from the box.

Stretching a spring with a load is an example of how a force can change the .................................... and the .................................... of an object.

Fig. 3.1 shows the vertical forces on a rocket.

Calculate the resultant force on the rocket.

resultant force = ........................................................... N

direction = ...........................................................

Fig. 3.2 shows the speed and direction of motion of an object at a point in time.

The resultant force on the object is zero for 10 seconds.

Deduce the speed and direction of motion after 5 seconds. Indicate the speed and direction of the object by drawing a labelled arrow next to the object in Fig. 3.3.

Fig. 3.1 shows a spring with no load attached. Fig. 3.2 shows the same spring with a load attached.

Describe how a student can determine the extension of the spring. You may draw on Fig. 3.1 and Fig. 3.2 as part of your answer.

The student plots a graph of load against extension, as shown in Fig. 3.3.

Calculate the mass that has a weight of 6.0 N.

Fig. 3.1 shows the horizontal forces acting on a swimmer.

size of resultant horizontal force = ...................................................... N

direction of resultant horizontal force = ......................................................    

[1]

[1]

[2]

Another swimmer weighs 700N. He stands on a diving board, as shown in Fig. 3.3.

Calculate the moment of the swimmer’s weight about point P.

A car travels around a circular track at constant speed.

Explain why it is incorrect to describe the circular motion as having constant velocity.

A force is required for the car to maintain the circular motion.

Explain why a force is required.

State the direction in which the force acts for objects in circular motion.

State the name of this force for the car on the track.

A 50 cm rule is balanced at its mid-point. A force of 8.0 N acts at a distance of 10 cm from one end of the rule.

Fig. 2.1 shows the arrangement.

Calculate the moment of the 8.0 N force about the pivot. Give the unit.

Another force acts at a point 10 cm from the pivot. It makes the rule balance.

  
On Fig. 2.1, draw an arrow to show the position and direction of this force.

A metre rule is balanced on a pivot by three vertical forces, as shown in Fig. 5.1.

Show that the moment of the 5.0 N force about the pivot is 200 N cm.

Calculate the size of force F.

Complete the statement by writing in the blank spaces.

 
The moment of a force about a pivot is equal to ............ multiplied by ............

Fig. 3.1 shows a horizontal rod of length 2.4 m and weight 160 N. The weight of the rod acts at its centre. The rod is suspended by two vertical ropes X and Y. The tension in each rope is 80 N.

Fig. 2.1 shows a man pushing down on a lever to lift one end of a heavy log.

State the term used to describe the turning force exerted by the man.

During a routine check of security camera footage at a zoo, it is discovered that a toucan and a grass snake have been escaping from their enclosures and performing experiments on a uniform 2 m long seesaw to study the principle of moments.

Fig. 1.1

Mass of a toucan = 600 g

Mass of a grass snake = 250 g

Calculate the weight of each animal in newtons. You may assume the acceleration of free fall is 10 m/s².

For the system in Fig. 1.1, calculate the clockwise and anticlockwise moments separately.

State whether the system is in equilibrium or not. Explain your reasoning.

On a different day, the toucan and the grass snake sit in new positions at different distances from the pivot. The same 2 metre long seesaw is not in equilibrium and has a resultant clockwise moment of 5.2 N m.

A bearded dragon climbs onto on the left side of the see saw. Suggest whether it is possible for the bearded dragon to bring the seesaw into equilibrium. Explain your answer using the principle of moments.

Average weight of a bearded dragon = 4.9 N

Fig. 8.1 shows a stationary horse and its rider, about to jump over two fences.

Fig. 8.1

Fig. 8.2 shows a side view of the horse.

Fig. 8.2

Fig. 8.3 shows a side view of the two fences. They both have the same height and a uniform density.

Fig. 8.3

[2] 

The total mass of the horse and rider is 520 kg. 
 

speed = ......................................................... [3]
 

height = ......................................................... [3]

The mass of a small steel ball is 120 g. The volume of the ball is 16.0 cm³.

Fig. 3.1 shows the vertical forces that act on a large plastic ball as it is falling.

A load is attached to a spring, as shown in Fig. 3.1. Two arrows indicate the vertical forces acting on the load. The spring and the load are stationary.

[1]

The load is pulled downwards and then released. The load moves up and down.

Fig. 3.2 represents the vertical forces acting on the load at some time after it is released.

Calculate the resultant force on the load and state its direction.

resultant force = ........................................................... N
direction = ............................................................... 

Fig. 1.1 shows an aeroplane accelerating uniformly on a runway. 

Fig. 1.1

The aeroplane has a mass of 3.1 × 10⁶ kg. 

From rest, the aeroplane reaches a speed of 70 m/s after 32 s.

Calculate the following quantities

When the aeroplane reaches its destination, air traffic control directs it to circle the airfield until there is a safe time to land.

Fig. 1.2 shows a head on view of the aeroplane flying at a constant speed in a circular horizontal path. 

Fig 1.2

Draw an arrow showing the resultant force on the aeroplane.

Explain your answer.

The pilot wants to decrease the radius of the circular flight path whilst maintaining a constant speed.

Suggest how the pilot could achieve this.

As the aeroplane lands on the runway, it decelerates from its top speed. The resultant force on the aeroplane is less than it was at take off. 

Explain why this is the case.

A resultant force acts on an object at rest. 

State the direction of the acceleration.

Extended

A resultant force acts perpendicularly on a object traveling at a constant speed. 

State the effect of the force on the object.

A man with a mass of 70 kg steps into an elevator. 

A tower crane has a load W, as shown in Fig. 3.1.

The counterweight has a weight of 80 000 N. This acts at a distance of 5.0 m from the pivot, as shown in Fig. 3.1.

Calculate the moment of the counterweight about the pivot. Give the unit.

The tower crane in Fig. 3.1 balances horizontally when holding the load W.

Calculate the weight of load W.

Fig. 2.1 shows a uniform plank AB of length 2.0 m suspended from two ropes X and Y.

The weight W of the plank is 210 N. The force in rope X is P. The force in rope Y is Q.

State, in terms of P, the moment of force P about B.

Calculate:

Fig. 4.1 shows a tractor fitted with a device for breaking up soil in a field.

The tractor has a heavy weight at the front. Explain why the heavy weight is needed.

[1]

Fig. 4.2 represents the weight of the device and its distance from the pivot. 

Calculate the moment of the weight of the device about the pivot. State the unit.

moment = ......................................................  [4]

In a double-decker bus there are two passenger compartments, one above the other.

Fig. 3.1 shows a double-decker bus on a tilted platform.

The platform is used to test the stability of the bus.

 
The angle the bus makes with the horizontal is gradually increased until the bus begins to topple to the left.

 
Explain why the bus begins to topple.

There are 30 passengers in the upper compartment of the bus and 2 passengers in the bottom compartment of the bus.

 
State how this affects the stability of the bus and the reason for this.

A university student is constructing some flat-pack furniture. 

An Allen key has a hexagonal end and is used to tighten hexagonal bolts. An Allen key can be used with its longer end in the hexagonal bolt, or can be rotated to place the shorter end in the hexagonal bolt. This is shown in Fig. 1.1.

Fig. 1.1

State which orientation, A or B, will allow the bolt to be tightened more easily. 

Explain why, referring to moments in your answer. 

The dimensions of the Allen key are shown in Fig. 1.2. 

Fig. 1.2

The student building the furniture applies a force of 150 N to the Allen key.

The student constructs the furniture but realises they need to lift it up to place a rug underneath. 

The furniture has a weight of 800 N and is too heavy for the student to lift.

Remembering a lecture about the principle of moments, they use a pivot and a plank of wood to lift it. As shown in Fig. 1.3, the furniture exerts a perpendicular force F_A on the plank, which is equal to 30% of the weight of the furniture. 

Fig. 1.3

Calculate the minimum force F_B the student must exert to lift the furniture.

The calculation in part (c) neglected the weight of the plank of wood.

Assuming the plank of wood has evenly distributed mass, explain how this would affect the size of the force that the student must exert to lift the furniture.