Solving Mechanics Problems: Forces, Friction, and Trigonometry Techniques

Mechanics Forces and Friction For more help visit our website https://www.exampaperspractice.co.uk/

Prior knowledge check 2) In the diagram below, calculate: 1) A particle of mass 5kg is acted on by two forces: 16.55 a) The length of the hypotenuse b) The size of ? ?1= 8? + 2? ? and ?2= 3? + 8? ? 25.02 Find the acceleration of the particle in the form ?? + ?? ?? 2 7 ? + 2? ?? 2 ? 15 For more help visit our website https://www.exampaperspractice.co.uk/

Teachings for Exercise 5A For more help visit our website https://www.exampaperspractice.co.uk/

Forces and Friction However, a force at an angle will have some effect in BOTH the horizontal and vertical directions! If a force at applied at an angle to the direction of motion you can resolve it to find the component of the force acting in the direction of motion O A O S H C H T A A horizontal force has no effect on the object in the vertical direction Opp = Sin x Hyp Adj = Cos x Hyp 10N Opp = Sin20 x 10 Adj = Cos20 x 10 Hyp Opp 10sin20 10N 20 Adj 10N 10cos20 A vertical force has no effect on the object in the horizontal direction So a force can be split into its horizontal and vertical components using Trigonometry! For more help visit our website https://www.exampaperspractice.co.uk/ 5A

Forces and Friction y If a force at applied at an angle to the direction of motion you can resolve it to find the component of the force acting in the direction of motion 9N 9Sin40 40 9Cos40 x Find the component of each force in the x and y-directions. Hence, write each force in the form ?? + ?? ? Force in the x-direction Force in the y-direction = 9Cos40 = 9Sin40 = 6.89N = 5.79N In vector form: 6.89? + 5.79? ? For more help visit our website https://www.exampaperspractice.co.uk/ 5A

Forces and Friction y If a force at applied at an angle to the direction of motion you can resolve it to find the component of the force acting in the direction of motion 12N 12Sin23 23 x Find the component of each force in the x and y-directions. 12Cos23 Hence, write each force in the form ?? + ?? ? Force in the x-direction Force in the y-direction In vector form: = 12Cos23 = 12Sin23 = 11.05N = 4.69N 11.05? + 4.69? ? = -11.05N (This will be negative as it is the opposite direction to x!) For more help visit our website https://www.exampaperspractice.co.uk/ 5A

Forces and Friction R Draw a diagram and label all forces 10N If a force at applied at an angle to the direction of motion you can resolve it to find the component of the force acting in the direction of motion 10sin30 30 8kg 10cos30 A box of mass 8kg lies on a smooth horizontal floor. A force of 10N is applied at an angle of 30 causing the box to accelerate horizontally across the floor. 8g In this example, the directions we are considering are horizontal (for movement) and vertical (for the normal reaction) Any forces which are not horizontal or vertical need to be split into their component parts in those directions a) Work out the acceleration of the box b) Calculate the normal reaction between the box and the floor In this case, that would be the diagonal force of 10N For more help visit our website https://www.exampaperspractice.co.uk/ 5A

Forces and Friction R Draw a diagram and label all forces 10N If a force at applied at an angle to the direction of motion you can resolve it to find the component of the force acting in the direction of motion 10sin30 30 8kg 10cos30 A box of mass 8kg lies on a smooth horizontal floor. A force of 10N is applied at an angle of 30 causing the box to accelerate horizontally across the floor. 8g To find the acceleration, we need to consider only horizontal forces, and then use ? = ?? ?( ) ? = ?? ? = 1.08 ?? 2 Sub in values a) Work out the acceleration of the box b) Calculate the normal reaction between the box and the floor 10???30 = (8)(?) Calculate 5 3 8 = ? Round to 3sf (or leave exact) This means we will resolve forces in the horizontal direction, with to the right as positive 1.08 = ? You need to indicate this when resolving For more help visit our website https://www.exampaperspractice.co.uk/ 5A

Forces and Friction R Draw a diagram and label all forces 10N If a force at applied at an angle to the direction of motion you can resolve it to find the component of the force acting in the direction of motion 10sin30 30 8kg 10cos30 A box of mass 8kg lies on a smooth horizontal floor. A force of 10N is applied at an angle of 30 causing the box to accelerate horizontally across the floor. 8g To find the normal reaction, we need to consider only vertical forces, and then use ? = ?? ?( ) Sub in values. Add on positive forces, subtract negative forces. The acceleration in the vertical direction is 0 ? = ?? ? = 1.08 ?? 2 a) Work out the acceleration of the box b) Calculate the normal reaction between the box and the floor ? + 10???30 8? = (8)(0) Rearrange ? = 8? 10???30 This means we will resolve forces in the vertical direction, with upwards as positive Calculate ? = 73.4? Without the force, the normal reaction would be the same as the weight of the box. You need to indicate this when resolving Since the force is pulling the box up slightly, this is why the normal reaction is less! For more help visit our website https://www.exampaperspractice.co.uk/ 5A

Forces and Friction 10N 10sin45 If a force at applied at an angle to the direction of motion you can resolve it to find the component of the force acting in the direction of motion 45 10cos45 8cos30 8sin30 30 8N Two forces, ? and ?, act upon a particle as shown in the diagram to the right. Work out the magnitude and direction of the resultant force. The resultant force vertically will be equal to: The resultant force horizontally will be equal to: 10???45 8???30 10???45 + 8???30 = 5 2 4(3.07 ) = 4 3 + 5 2(13.99 ) You can solve this method as before, by splitting each force into their horizontal and vertical components 14.3? 3.07? So the resultant force is of magnitude 14.3N at an angle of 12.4 above the horizontal 12.4 ? Magnitude Angle ? 13.99? 3.07 13.99 (13.99)2+(3.07)2 = = ??? 1 = 14.3? For more help visit our website https://www.exampaperspractice.co.uk/ = 12.4 5A

Forces and Friction 10N If a force at applied at an angle to the direction of motion you can resolve it to find the component of the force acting in the direction of motion 45 30 8N Two forces, ? and ?, act upon a particle as shown in the diagram to the right. Work out the magnitude and direction of the resultant force. Draw forces one after another 30 10N 105 45 30 8N Alternatively, you can solve this by using a triangle of forces You will then need to find an angle inside the triangle, and use the sine or cosine rule Start by drawing the forces as a chain ie draw one first, and draw the second after, starting from the end point of the first force For more help visit our website https://www.exampaperspractice.co.uk/ 5A

Forces and Friction 10N If a force at applied at an angle to the direction of motion you can resolve it to find the component of the force acting in the direction of motion 45 30 8N Two forces, ? and ?, act upon a particle as shown in the diagram to the right. Work out the magnitude and direction of the resultant force. You will then need to find an angle inside the triangle, and use the sine or cosine rule 14.3? 30 10N 105 Alternatively, you can solve this by using a triangle of forces 8N ?2= ?2+ ?2 2?????? Start by drawing the forces as a chain ie draw one first, and draw the second after, starting from the end point of the first force Sub in values ?2= (8)2+(10)2 2 8 (10)???105 Calculate ? = 14.3? For more help visit our website https://www.exampaperspractice.co.uk/ 5A

Forces and Friction 10N If a force at applied at an angle to the direction of motion you can resolve it to find the component of the force acting in the direction of motion 45 30 8N Two forces, ? and ?, act upon a particle as shown in the diagram to the right. Work out the magnitude and direction of the resultant force. You will then need to find an angle inside the triangle, and use the sine or cosine rule 14.3? 30 10N 105 Alternatively, you can solve this by using a triangle of forces 8N ???? ? =???? ? Sub in values Start by drawing the forces as a chain ie draw one first, and draw the second after, starting from the end point of the first force ???? 10 =???105 14.3 Calculate ???? = 0.675 Calculate Subtract 30 to find the angle above the horizontal ? = 42.4 For more help visit our website ????????? = 12.4 https://www.exampaperspractice.co.uk/ 5A

Forces and Friction 140N 100N If a force at applied at an angle to the direction of motion you can resolve it to find the component of the force acting in the direction of motion 140sin45 100sin30 45 30 Pcos 100cos30 Psin 140cos45 Three forces act on a particle as shown. Given that the particle is in equilibrium, calculate the magnitude of ? and the value of ?. P ? = ?? ?( ) Sub in values 100???30 + ????? 140???45 = 0 Rearrange Split each force into its horizontal and vertical components ????? = 140???45 100???30 Then, resolve horizontally and vertically. If the particle is in equilibrium then there is no acceleration in any direction ? = ?? ?( ) Sub in values ????? 100???30 140???45 = 0 Rearrange ????? = 140???45 100???30 ????? = 100???30 + 140???45 ????? = 100???30 + 140???45 For more help visit our website https://www.exampaperspractice.co.uk/ 5A

Forces and Friction 140N 100N If a force at applied at an angle to the direction of motion you can resolve it to find the component of the force acting in the direction of motion 140sin45 100sin30 45 30 Pcos 100cos30 Psin 140cos45 Three forces act on a particle as shown. Given that the particle is in equilibrium, calculate the magnitude of ? and the value of ?. P 1) ????? = 100???30 + 140???45 2) ????? = 140???45 100???30 Split each force into its horizontal and vertical components 1) 2) ???? =100???30 + 140???45 140???45 100???30 Then, resolve horizontally and vertically. If the particle is in equilibrium then there is no acceleration in any direction Calculate ? = 85.2 You can use this value in either 1) or 2) to find the value of P ? = 150? For more help visit our website https://www.exampaperspractice.co.uk/ 5A

Teachings for Exercise 5B For more help visit our website https://www.exampaperspractice.co.uk/

Forces and Friction Note that when using an inclined plane, we use the terminology parallel for movement direction and perpendicular for the normal reaction You can extend this process to particles on an inclined plane, by considering forces parallel and perpendicular to the plane This is actually exactly the same as with a horizontal plane! (horizontal = parallel and vertical = perpendicular) Inclined plane Horizontal plane Normal reaction Normal reaction Direction of movement Weight Weight We resolve parallel to the plane for the direction of movement We resolve perpendicular to the plane for the normal reaction The weight still acts vertically For more help visit our website https://www.exampaperspractice.co.uk/ We resolve horizontally for the direction of movement We resolve vertically for the normal reaction The weight acts vertically 5B

Forces and Friction R You can extend this process to particles on an inclined plane, by considering forces parallel and perpendicular to the plane 60 3gCos30 30 When an object is on an inclined plane, we consider the forces acting parallel to the plane and perpendicular to the plane (instead of vertically and horizontally) 3g 30 90 3gSin30 Above is a box resting on a plane inclined at an angle of 30 to the horizontal Label gravity, which always acts vertically downwards This is because any movement will be parallel to the plane (and we always then consider the direction which is perpendicular to any movement) Gravity must then be split into the parallel and perpendicular components (rather than horizontal and vertical) The angle in the triangle created is the same as the angle the plane is inclined at (if you work out angles you can see why!) Make sure you think carefully about which is Sine and which is Cosine! Don t forget the normal reaction, and any other forces which are involved in the question! However, gravity will always work in a vertical direction so must be split into parallel and perpendicular directions For more help visit our website https://www.exampaperspractice.co.uk/ 5B

Forces and Friction R 2N You can extend this process to particles on an inclined plane, by considering forces parallel and perpendicular to the plane 2gCos20 20 2g A box of mass 2kg is resting on a smooth plane inclined at an angle of 20 to the horizontal. It meets resistance of 2N as it travels down the slope a) Calculate the acceleration of the box down the slope b) If the box starts 10m up the plane, calculate the velocity of the box at the bottom of the plane 20 2gSin20 Resolve parallel to the plane ?( ) ? = ?? Sub in values and resolve parallel 2????20 2 = (2 ?) Work out some parts (to keep accuracy) Round to 2sf as gravity is given to this degree of accuracy 19.6???20 2 = 2? 2.4 = ? (2??) For more help visit our website https://www.exampaperspractice.co.uk/ 5B

Forces and Friction R 2N You can extend this process to particles on an inclined plane, by considering forces parallel and perpendicular to the plane 2gCos20 20 2g A box of mass 2kg is resting on a smooth plane inclined at an angle of 20 to the horizontal. It meets resistance of 2N as it travels down the slope a) Calculate the acceleration of the box down the slope 2.4ms-2 b) If the box starts 10m up the plane, calculate the velocity of the box at the bottom of the plane 20 2gSin20 ? = 10 ? = 0 ? =? ? = 2.4 ? =? ?2= ?2+ 2?? Sub in values Remember to use the exact value for a, not the rounded one! ?2= 02+ 2(2.4)(10) ?2= 02+ 2(2.4)(10) Calculate ?2= 47.03 Square root ? = 6.6?? 1 (2??) For more help visit our website https://www.exampaperspractice.co.uk/ 5B

Forces and Friction R 2N You can extend this process to particles on an inclined plane, by considering forces parallel and perpendicular to the plane 2gCos20 20 2g A box of mass 2kg is resting on a smooth plane inclined at an angle of 20 to the horizontal. It meets resistance of 2N as it travels down the slope a) Calculate the acceleration of the box down the slope 2.4ms-2 b) If the box starts 10m up the plane, calculate the velocity of the box at the bottom of the plane - 6.6ms-1 c) Find the normal reaction between the box and the plane 20 2gSin20 Resolve perpendicular to the plane ?( ) ? = ?? Sub in values and resolve perpendicular (no acceleration in this direction) ? 2????20 = (2 0) Rearrange ? = 2????20 Round to 2sf as gravity is given to this degree of accuracy ? = 18? For more help visit our website https://www.exampaperspractice.co.uk/ 5B

Forces and Friction ? Ensure you label all forces and split into their parallel and perpendicular components You can extend this process to particles on an inclined plane, by considering forces parallel and perpendicular to the plane ??? 2????? ? 2? 4? A particle P of mass 2kg is moving on a smooth slope and is being acted on by a force of 4N that acts parallel to the slope as shown. ? 2????? Remember that ???? =??? ??? The slope is inclined at an angle ? to the horizontal, where ???? =3 out the acceleration of the particle. In this case, ???? =3 5 4. Work 3 4 So draw a triangle with angle ?, opposite side 3 and adjacent side 4 ? 4 You will often encounter questions where the angle is given in this way. A good starting point is to find the corresponding values of ???? and ???? So the hypotenuse will be 5 ???? =??? ???? =??? ??? ??? ???? =3 ???? =4 5 5 For more help visit our website https://www.exampaperspractice.co.uk/ 5B

Forces and Friction ???? =3 ? Ensure you label all forces and split into their parallel and perpendicular components 5 You can extend this process to particles on an inclined plane, by considering forces parallel and perpendicular to the plane ???? =4 ??? 5 2????? ???? =3 ? 2? 4 4? A particle P of mass 2kg is moving on a smooth slope and is being acted on by a force of 4N that acts parallel to the slope as shown. ? 2????? Resolve parallel to the plane The slope is inclined at an angle ? to the horizontal, where ???? =3 out the acceleration of the particle. ?( ) ? = ?? Sub in values and resolve parallel (you can choose up or down the slope) 4. Work 2????? 4 = (2 ?) We can use values for ? and ???? 3 5 2 9.8 4 = 2? Now resolve parallel to the plane Calculate 3.9 = ? (2??) If we had resolved up the slope instead, the acceleration would have been negative You can interpret this as being in the opposite direction to the resolving For more help visit our website https://www.exampaperspractice.co.uk/ 5B

Forces and Friction ? You can extend this process to particles on an inclined plane, by considering forces parallel and perpendicular to the plane Ensure you label all forces and split into their parallel and perpendicular components 5? ? ?? 60 5????60 ?????30 30 ?? A particle of mass ? is pushed up a smooth slope by a force of magnitude 5g acting at an angle of 60 to the slope. This causes the particle to accelerate up the slope at 0.5ms-2. 30 ?????30 Resolve parallel to the plane ?( ) ? = ?? Sub in values Show that the mass of the particle is 5? 1+? ?? 5????60 ?????30 = (?)(0.5) Add ?????30 5????60 = 0.5? + ?????30 Cos60 and Sin30 are both equal to 0.5 Resolve parallel to the plane 2.5? = 0.5? + 0.5?? Multiply by 2 Since the particle is accelerating up the slope, it makes sense to take this as the positive direction 5? = ? + ?? Factorise right side 5? = ?(1 + ?) Divide by the bracketed part 5? 1 + ?= ? For more help visit our website https://www.exampaperspractice.co.uk/ 5B

Teachings for Exercise 5C For more help visit our website https://www.exampaperspractice.co.uk/

Forces and Friction You can calculate the magnitude of a frictional force using the coefficient of friction Friction is a force which opposes movement between two rough surfaces. It is dependent on two things: 1) The normal reaction between the two surfaces 2) The coefficient of friction between the two surfaces The maximum frictional force is calculated as follows: ? = ??????????? ?? ???????? ????= ?? ? = ? ? ?????? ???????? If a surface is described as smooth , the implication is that the coefficient of friction is 0. For more help visit our website https://www.exampaperspractice.co.uk/ 5C

Forces and Friction a ms-2 Draw a diagram You can calculate the magnitude of a frictional force using the coefficient of friction R Friction is a force which opposes movement between two rough surfaces. F 5kg 10N ? = ??????????? ?? ???????? ????= ?? 5g N ? = ? ? ?????? ???????? We need to find the maximum possible frictional force To do this we need R, the normal reaction A block of mass 5kg is lying at rest on rough horizontal ground. The coefficient of friction between the block and the ground is 0.4. A horizontal force, P, is applied to the block. Find the magnitude of the frictional force acting on the block and its acceleration when: ? = ?? ?( ) Resolve vertically ? 5? = (5 0) Calculate R ? = 5? (49?) Now we can calculate the maximum possible frictional force a) P = 10N b) P = 19.6N c) P = 30N ????= ?? Sub in values ????= (0.4 49) Calculate FMAX For more help visit our website https://www.exampaperspractice.co.uk/ ????= 19.6? 5C

Forces and Friction a ms-2 Draw a diagram You can calculate the magnitude of a frictional force using the coefficient of friction ????= 19.6? R Friction is a force which opposes movement between two rough surfaces. 10N F 5kg 10N ? = ??????????? ?? ???????? ????= ?? 5g N ? = ? ? ?????? ???????? The maximum frictional force is 19.6 N Any force will be opposed by friction up to this value For part a), the force is only 10N Therefore, the frictional force will match this at 10N, preventing movement Hence, there is also no acceleration A block of mass 5kg is lying at rest on rough horizontal ground. The coefficient of friction between the block and the ground is 0.4. A horizontal force, P, is applied to the block. Find the magnitude of the frictional force acting on the block and its acceleration when: a) P = 10N b) P = 19.6N c) P = 30N For more help visit our website https://www.exampaperspractice.co.uk/ 5C

Forces and Friction a ms-2 Draw a diagram You can calculate the magnitude of a frictional force using the coefficient of friction ????= 19.6? R Friction is a force which opposes movement between two rough surfaces. 19.6N F 5kg 19.6N ? = ??????????? ?? ???????? ????= ?? 5g N ? = ? ? ?????? ???????? The maximum frictional force is 19.6 N Any force will be opposed by friction up to this value For part b), the force is only 19.6N Therefore, the frictional force will match this at 19.6N, preventing movement Hence, there is also no acceleration A block of mass 5kg is lying at rest on rough horizontal ground. The coefficient of friction between the block and the ground is 0.4. A horizontal force, P, is applied to the block. Find the magnitude of the frictional force acting on the block and its acceleration when: a) P = 10N b) P = 19.6N c) P = 30N This situation is called limiting equilibrium , as the object is on the point of movement For more help visit our website https://www.exampaperspractice.co.uk/ 5C

Forces and Friction a ms-2 Draw a diagram You can calculate the magnitude of a frictional force using the coefficient of friction ????= 19.6? R Friction is a force which opposes movement between two rough surfaces. 19.6N F 5kg 30N ? = ??????????? ?? ???????? ????= ?? 5g N ? = ? ? ?????? ???????? For part c), the force is 30N The frictional force will oppose 19.6N of this, but no more. Hence, the object will accelerate Resolve horizontally! A block of mass 5kg is lying at rest on rough horizontal ground. The coefficient of friction between the block and the ground is 0.4. A horizontal force, P, is applied to the block. Find the magnitude of the frictional force acting on the block and its acceleration when: ?( ) ? = ?? Sub in values and resolve horizontally 30 19.6 = 5 ? a) P = 10N b) P = 19.6N c) P = 30N Calculate 10.4 = 5? Divide by 5 2.08 = ? So the acceleration will be 2.08ms-2 For more help visit our website https://www.exampaperspractice.co.uk/ 5C

Forces and Friction R Draw a diagram You can calculate the magnitude of a frictional force using the coefficient of friction F 5kg P Friction is a force which opposes movement between two rough surfaces. 5g N ? = ??????????? ?? ???????? ????= ?? Resolve vertically to find the normal reaction ? = ? ? ?????? ???????? ? = ?? ?( ) Sub in values and resolve vertically A 5kg box lies at rest on a rough horizontal floor. The coefficient of friction between the box and the floor is 0.5. A force P is applied to the box. Calculate the value of P required to cause the box to accelerate if: ? 5? = (5 0) Calculate ? = 49? Now find the maximum frictional force a) P is applied horizontally b) P is applied at an angle of above the horizontal, where tan = 3/4 ????= ?? Sub in values ????= (0.5 49) Calculate ????= 24.5? For more help visit our website https://www.exampaperspractice.co.uk/ 5C So P will have to exceed 24.5N to make the object move!

Forces and Friction Draw a diagram R P You can calculate the magnitude of a frictional force using the coefficient of friction Psin 0.6P F 5kg Pcos 0.8P Friction is a force which opposes movement between two rough surfaces. 5g N ? = ??????????? ?? ???????? ????= ?? We need to find the values of Cos and Sin . The ratio for Tan can be used to find these! ? = ? ? ?????? ???????? A 5kg box lies at rest on a rough horizontal floor. The coefficient of friction between the box and the floor is 0.5. A force P is applied to the box. Calculate the value of P required to cause the box to accelerate if: O A O Tan = 3/4 S H C H T A So Opp = 3 And Adj = 4 Hyp We can find the hypotenuse using Pythagoras Theorem! 5 3 Opp a) P is applied horizontally 24.5N b) P is applied at an angle of above the horizontal, where tan = 3/4 4 Adj Sin = 3/5 Sin = 0.6 Cos = 4/5 Cos = 0.8 For more help visit our website https://www.exampaperspractice.co.uk/ 5C

Forces and Friction Draw a diagram R P You can calculate the magnitude of a frictional force using the coefficient of friction 0.6P F 5kg 0.8P Friction is a force which opposes movement between two rough surfaces. 5g N ? = ??????????? ?? ???????? Resolve vertically to find the normal reaction ????= ?? ? = ? ? ?????? ???????? ? = ?? ?( ) Sub in values and resolve vertically We find the normal reaction in terms of P ? + 0.6? 5? = (5 0) A 5kg box lies at rest on a rough horizontal floor. The coefficient of friction between the box and the floor is 0.5. A force P is applied to the box. Calculate the value of P required to cause the box to accelerate if: ? = 49 0.6? Now find the maximum frictional force ????= ?? a) P is applied horizontally 24.5N b) P is applied at an angle of above the horizontal, where tan = 3/4 Sub in values Find Fmax in terms of P ????= 0.5(49 0.6?) ????= 24.5 0.3? So, 0.8P will have to exceed this if the box is to move For more help visit our website https://www.exampaperspractice.co.uk/ 5C

Forces and Friction Draw a diagram ????= 24.5 0.3? R P You can calculate the magnitude of a frictional force using the coefficient of friction 0.6P 24.5 0.3P F 5kg 0.8P Friction is a force which opposes movement between two rough surfaces. 5g N ? = ??????????? ?? ???????? We need to find the value for P for which the box is in limiting equilibrium that is, so the horizontal forces cancel each other out ????= ?? ? = ? ? ?????? ???????? Resolve horizontally A 5kg box lies at rest on a rough horizontal floor. The coefficient of friction between the box and the floor is 0.5. A force P is applied to the box. Calculate the value of P required to cause the box to accelerate if: ?( ) ? = ?? Sub in values and resolve horizontally Careful with the bracket! Rearrange and solve 0.8? (24.5 0.3?) = (5 0) 0.8? 24.5 + 0.3? = 0 a) P is applied horizontally 24.5N b) P is applied at an angle of above the horizontal, where tan = 3/4 1.1? = 24.5 ? = 22? (2??) P must exceed 22N, which is less than when P was horizontal The reason is because some of the force is upwards, this alleviates some of the friction between the surfaces https://www.exampaperspractice.co.uk/ For more help visit our website 5C

????= ?? Forces and Friction ?(2????30) ???????? 2????30 ? Draw and fully label a diagram! You can calculate the magnitude of a frictional force using the coefficient of friction ??? A particle of mass 2kg is sliding down a rough slope that is inclined at 30 to the horizontal. Given that the acceleration of the particle is 1ms-2, find the coefficient of friction, ?, between the particle and the slope. 2????30 30 2? 30 2????30 Resolve perpendicular to find the normal reaction Although we are trying to find the coefficient of friction, this does not change how we approach the question ? = ?? ?( ) Sub in values and resolve perpendicular ? 2????30 = (2 0) We find the normal reaction in terms of P Start by finding the normal reaction ? = 2????30 Then find an expression for the frictional force Now find the maximum frictional force ????= ?? Sub in R Then add this to the diagram ????= ?(2????30) Since the particle is moving, the friction must be at this level For more help visit our website https://www.exampaperspractice.co.uk/ Add this information to the diagram 5C

????= ?? Forces and Friction ?(2????30) 2????30 Draw and fully label a diagram! You can calculate the magnitude of a frictional force using the coefficient of friction ??? A particle of mass 2kg is sliding down a rough slope that is inclined at 30 to the horizontal. Given that the acceleration of the particle is 1ms-2, find the coefficient of friction, ?, between the particle and the slope. 2????30 30 2? 30 2????30 Resolve parallel to the plane ?( ) ? = ?? Sub in values and resolve perpendicular 2????30 ?(2????30) = (2 1) Rearrange to isolate ? 2????30 (2 1) = ?(2????30) Divide by 2????30 2????30 (2 1) 2????30 = ? Calculate 0.46 = ? Remember that your answer should be between 0 and 1! For more help visit our website https://www.exampaperspractice.co.uk/ 5C