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physics Advanced Subsidiary (AS) Level Physics.
 
Solved problems for the chapter:
 

Turning Effects of Forces

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Example 1.

Four weights of masses 1 kg, 2 kg, 3 kg, and 4 kg are placed in the x, y coordinate system so that the weights are arranged on the corners of a square with a side length of 1 m. Calculate the coordinates of the centre of gravity.

    
Example 2.

A cylinder with a weight of 600 N and a radius of 0.6 m is to be pulled over a 10 cm high step. The line of action of the force is on the axis of rotation of the cylinder. How much force do we need?

    
3.

A system of two geometric bodies of the same substance and the same thickness joined to each other is shown in the figure below. The first body is a cuboid with a cross-section of 20 cm x 4 cm, and the second is a cylinder with a radius of 6 cm. Calculate the centre of gravity of the system.


A system of two geometric bodies

    
4.

A wheel of radius 0.8m is rotated with a force to lift a bucket of water of mass 20kg from a well. The radius of the shaft on which the rope of the bucket is wound is 6 cm. With what force do we have to turn the wheel to make the bucket rise uniformly?

    
5.

A load of 60 kg is hung on a 3 m long horizontal light pole at a distance of 1 m from one of its ends. The pole is then placed on two pillars. How much force does each pillar exert on the pole? What is the torque of the weight of the load on the pillar that carries more weight?

    
6.

A 6 m long rod weighing 60 kg is supported on one-third of its length. The shorter end is attached to a base with a rope. At the other end of the rod is a load weighing 40 kg. What is the force in the rope?

    
7.

A 2 m long wooden rod weighs 2 kg. A 2 dm long metal rod is attached to one end of the rod. What must be the mass of the metal rod for the centre of gravity of the combination to be at the junction of the two rods?

    
8.

Let's consider the basic application of a typical screwdriver. The radius of the screwdriver handle is 3 cm and the tip of the screwdriver has a radius of 3 mm. If we act on the screwdriver with a force of 10 N, with what force does the tip of the screwdriver act on the screw?

    

9.

A mass of 200 g rotates in a vertical plane on a string 1 m long. What is the torque of the force of gravity when the weight is at the top, on the horizontal plane, and when the string encloses an angle of with the horizontal plane?

    
10.

On the floor, there is a built-in square hatch with a side 50 cm long and weighing 30 kg. An opening rope is attached at one end and hinges at the opposite edge. The hatch is opened through an angle of to the horizontal. What is the tension in the rope with which we opened the hatch?


Opened hatch

    
11.

A screw is to be tightened with a torque of 200 N m, what should be the length of the screw if it can be pressed with a force of 500 N?

    
12.

A picture measuring 80 cm by 50 cm hangs on the wall as shown in the picture. A force of 20 N acts on the lower-left corner of the image. The angle between the force and the lower edge of the image is . Calculate the moment of the force on the image. The weight of the image is neglected.


    
13.

If we try to topple over a cuboid with edges of lengths a = 5 cm, b = 10 cm and c = 15 cm, over which edge do we do this with the least force?

    
14.

A 4 t crane lifts a load of 1800 kg with a light, 5 m long lever as shown in the figure. The length of the crane without the lever is 4 m. At what angle could the lever lift the load to keep it from tipping over?


    
15.

A mason's hammer is used to pull a nail which resists with a force of 1200 N. The length of the hammer head is 15 cm. The nail is set at the hook of the hammer head which is 5 cm away from the left end of the hammer head as shown below. How much force do we have to apply on the 30 cm long handle of the hammer to pull the nail?


Hammer and nail

    
16.

An 80 cm long stick is placed on the floor as shown below. It is acted upon by two equal and opposite forces of magnitude 9 N each. The rod is rotatable about the marked pivot point. Ignoring any friction and considering the geometry in the figure, what is the total torque for each case? In which of the examples shown is the total torque greatest?


A stick under the influence of two equal and opposite forces

    
17.

A tractor moves transversely on a slope inclined at an angle of to the horizontal. The distance between the wheels of the tractor is 150 cm. How high can the tractor's centre of gravity be to prevent it from tipping over?

    
18.

What force must be used to lift a pole of mass 10 kg at one end if it remains on the ground at the other end?

    

19.

A cyclist applies a force of 200 N on the pedals of his bicycle. The pedal is at a distance of 20 cm from the axis. On the axle, there is a gear with 52 teeth and it is connected via a chain to a gear with 13 teeth and a radius of 2 cm. This smaller gear is mounted on the rear drive wheel with a radius of 50 cm. What is the force with which the bicycle is driven on the road?


Pedal, chain and drive wheel

    
20.

An 80 kg teacher stands 3 m from the right edge of a 5 m long board weighing 10kg.

  • Calculate the forces in the supports if the supports are at the ends of the rod.

  • Where should a student weighing 40 kg stand so that the forces in the supports are the same?

    
21.

A log weighing 250 kg lies in a groove, with an angle at the bottom. With what force do we have to act on the log in the tangential direction in order to rotate the log in the groove? The coefficient of friction between the log and the groove is 0.34.


Log in a groove

    
22.

A circular plate with a diameter of 70 cm has a circular hole of radius 7 cm whose centre is at a distance from centre of the plate. Calculate how much the centre of gravity of the plate is displaced from its centre.


Circular plate with hole

    
23.

A 2 m long rod can be attached to the ceiling at both ends with springs. The springs have force constants of 4 and 600 . The spring at the right end is stiffer. How far from the left edge of the rod do we need to hang a 1.5 kg mass on it to keep the rod horizontal?


Springs and rod

    
24.

The stand in the picture is more loaded on the left side and is therefore unstable.




The figure shows two weights - the smaller is 2 kg and the larger is 14 kg. The mass of the stand is negligible. How much extra weight do we have to add to either of the points 5, 6, 7, or 8 to keep the stand stable?

    
25.

A light board 4 m long is supported at both ends by two pillars. An object acting on a board with a force of 600 N is placed at a distance of 1 m from the left pillar. What are the forces on both pillars?

    
26.

A bridge with a total length of 60 m is supported by two symmetrically placed supporting pillars, which are 20 meters apart. There are currently two vehicles on the bridge. A car weighing 1500 kg is 10 m away from the right end of the bridge. A van, which weighs 4 t, is driving in the opposite direction and is located 15 m from the left end of the bridge. Calculate the force on each pillar.

    
27.

A light bar is placed horizontally between two vertical beams as shown in the figure below. The coefficient of friction between the beams and the bar is 0.6. At what minimum angle can we pull the bar to keep it from slipping?


Light bar between two beams