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

Systems in Equilibrium

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Newton's First Law of Motion for KS4
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Introduction to Force
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Torque
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:systems_in_equilibrium/5136/


Example 1.

Four perpendicular forces of magnitudes 80 N, 40 N, 60 N, and 20 N act on a ball. Find the fifth force that can act with the four other forces on the ball so that the ball moves uniformly and in a straight line.


    
Example 2.

A string is attached to the ceiling at both ends so that it is at an angle on the left-hand side and on the right-hand side, to the ceiling- see the figure below. A 4 N weight is hung on the string. Graphically determine what the forces are in both parts of the string?


    
3.

On a wall hangs a picture in a frame weighing 2 kg with a string attached to the frame on two sides such that the string encloses an angle of with respect to the upper edge of the frame - see figure. With how much force do both ends of the string hold the image?


    
4.

A folding shelf is attached to the wall. At an angle is a rope that holds the shelf in a horizontal position - see picture. The rope can withstand a maximum force of 100 N. If we place a package weighing 5 kg on the shelf, will the rope break?


    
5.

James stands at the top of a ladder as shown in the picture. His weight is 500 N. With what forces do the load-bearing columns of the ladder act on the base if the angle between the legs of the ladder is ? We ignore the weight of the ladder.


    
6.

A sphere lies on a flat surface. Two perpendicular forces of magnitude 12 N each begin to act on it.

  • What is the resultant of both forces?

  • Which direction will the ball move and is the movement uniform or not?

  • How much force do we need to add to keep the movement uniform?

    
7.

A string is attached to the ceiling at one end and to the wall at the other end, as shown in the figure. The angle between the string and the ceiling is , and between the string and the wall is . A weight of 60 N is hung on the string. What is the force in each part of the string?


    
8.

Two forces of magnitudes 80 N and 60 N act on a body at an angle to each other. What is the magnitude of the third force that can be added to the two forces so that the body moves uniformly and in a straight line?


    

9.

A ball rests on the table - Figure A. No traction or thrust is applied to it. At some point, three equal forces of magnitude 4 N begin to act on the ball. The angle between each pair of these forces is - Figure B. What will be the motion of the ball after the forces start to act?


    
10.

A shelf with a brace is attached to the wall as shown in the picture. At the edge of the shelf is a load weighing 100 N. What are the forces on the shelf and the brace?


Attached shelf with bracket

    
11.

The body slides uniformly and in a straight line at a speed of 3 m/s. At some point, two equal and perpendicular forces of magnitude 4 N each begin to act on it - see figure. How does the speed of motion of the body change? What force should be added to both forces to maintain the speed and direction of motion?


    
12.

A rope is attached to the ceiling on one side and passed over the attached pulley on the other side. Between the attached end of the rope and the pulley hangs a body of weight , and on the other side of the pulley is a body of weight - see the figure below. The system is in equilibrium. Calculate the angle between the rope and the horizontal axis.


    
13.

Three bodies are attached to a rope and hung via two attached pulleys as shown in the figure below. The weights of the second and third bodies are 10 N and 18 N respectively.

  • What is the angle of the right side of the rope with respect to the horizontal?

  • What must be the weight of the first body for the left side of the rope to be horizontal?


    
14.

  • State the two conditions that must be satisfied for a body to be in equilibrium.


  • Three co-planar forces act on a body that is in equilibrium.

    • Describe how to draw a vector triangle to represent these forces

    • State how the triangle confirms that the forces are in equilibrium.


  • A weight of hangs vertically by two strings AB and AC, as shown in the figure below




    For the weight to be in equilibrium, the tension in string AB is and in string AC it is . On the above figure, draw a vector triangle to determine the magnitudes of and .


  • By reference to the figure, suggest why the weight could not be supported with the strings AB and AC both horizontal.


    
15.

An object, made from two equal masses joined by a light rod, falls with uniform speed through air. The rod remains horizontal. Which statement about the equilibrium of the system is correct?


  • It is not in equilibrium because it is falling steadily.


  • It is not in equilibrium because it is in motion.


  • It is not in equilibrium because there is a resultant torque.


  • It is in equilibrium because there is no resultant force and no resultant torque.

    
16.

Forces are applied to a rigid object. The forces all act in the same plane. In which diagram is the object in equilibrium?


    
17.

An object is suspended by two ropes. One rope has a tension of at an angle of to the horizontal. The other rope has a tension of at an angle of to the horizontal.




The object is in equilibrium. What is the mass of the object?









    
18.

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?

    

19.

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?

    
20.

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?

    
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 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