# Search results

1. ### To find the resultant of forces on a lamina

Could I please ask for help with the following question: A lamina is in the shape of an equilateral triangle ABC, and D, E, F are the midpoints of BC, CA, AB respectively. Forces of magnitude 4N, 8N, 4N, 3N, 3N act along AB, BC, CA, BE, CF respectively, the direction of each force being...
2. ### To calculate torque on a supported beam

Could I please ask for help with the last part of the following question? I have the first two parts done, answers are: Distance of COG from A = a(1+n)/n and W1 = W(1+n)/3 I can't see how to go about the last part. Here's my diagram for the system prior to the torque L being added: In...
3. ### How to calculate the magnitudes of three forces around a hexagon

Can anyone please help me with the following? Three forces which act along the sides AB, BC and CD of a regular hexagon ABCDEF of side 2a, have a resultant which acts along DF. When a couple of 4Pa in the sense CBA is added in the plane of the hexagon, the resultant acts along CA. Find the...
4. ### To find the magnitude of the resultant of forces around a triangle

Could I please ask for advice with the following: ABC is a right-angled triangle in which AB = 4a; BC = 3a. Forces of magnitudes P, Q and R act along the directed sides AB, BC and CA respectively. a) Find the ratios P:Q:R if their resultant is a couple. b) If the force along the directed line...
5. ### To find the ratio of forces around a right triangle

Could I please ask for help with the following: ABC is a right-angled triangle in which AB = 4a; BC = 3a. Forces of magnitudes P, Q and R act along the directed sides AB, BC and CA respectively. Find the ratios P:Q:R if their resultant is a couple. Book answer is 4 : 3 : 5 Here's my diagram...
6. ### Forces proportional to the sides of a quadrilateral result in a couple

Can I please ask for help with the following: Forces proportional to the sides of a quadrilateral taken in order act respectively along those sides. Prove that the resultant of the system is a couple whose magnitude is represented by twice the area of the quadrilateral. Not sure where to start...
7. ### To find the equivalent force

Could any one please help with the following? Three forces of magnitudes 10, 3 * sqrt(5) and 25 newtons act along lines whose vector equations are respectively: r1 = i - 2j + k(4i + 3j) , r2 = -2i + 4j + k(2i - j) and r3 = 4i + k(7i - 24j) A fourth force F4 is introduced which reduces the...
8. ### To find the relative velocity of the wind as seen from a car

Could I please ask for any help with the following question: Here's my attempt: (i and j are unit vectors in the directions of east and north respectively) (apologies that LaTeX is simply not working for me, I'll label the angles in each case T and P as shown in my diagram) Let the...
9. ### To find the relative velocities of linear and circular motion

Could I please ask for help regarding the final part of the following question: It is the very last part, to find v in terms of u. So I have that the velocity of the midpoint of XY is: V_m = (u/2) i + (u/2) j I let the position vector of P be: r_p = cos(wt) i + sin(wt) j (w = angular...
10. ### Calculating the time to cross a river

Could I please ask for help on the last part of this question: So, part b, I get the right time but not the right distance. Book answers are: distance = 1/6 and time = a/V. Here's my (faulty?) reasoning (LaTeX isn't working for me): The boat is steered due east and so would have a velocity...
11. ### To find the time to nearest appoach of a dinghy and a buoy

Can anyone please help me see if my reasoning is correct regarding the following question? I'll just solve for the case where the dinghy tracks so as to just 'touch' the exclusion zone on the 'high' side So, in the diagram below: The dinghy tracks along the red path, inclined at x degrees...
12. ### To find the closest approach of two ships

Could I please ask for help regarding the last part of this question: At a given instant, a ship P revelling due east at a speed of 30km/h is 7km due north of a second ship Q which is travelling x degrees west of north at a speed of 14km/h, where tan(x)=3/4. Show that the speed of Q relative to...
13. ### To find the time for which a vessel is within range of these guns

Could I please ask for help with the following question (the second part): A cruiser sailing due north at 24 km/h sights a destroyer 48 km due east sailiing at 56 km/h on a course (360-a) degress where cos(a)=11/14. Show that the destroyer's course realtive to the cruiser is on a bearing of...
14. ### To find the true velocity of wind from relative velocity

Please can I ask for help with the following as to where I'm going wrong. Book answer is 20 knots and 315 degrees My solution: In the below diagram I have sketched the two situations, k is the true speed of the wind. First question is, is my diagram correct? The velocity of the wind...
15. ### To find the time taken for one vessel to reach another

Could I please ask for help regarding my answer to the following question? I've done the first part and get the answer of 500 seconds. I anticipated no problem with the second part, it is the same problem with different inputs, but I have disagreed with the provided answer of 1754 seconds. I...
16. ### The closest approach of two ships

Could I please ask for help with the following question: A destroyer moving on a breaing of 30 degrees at 50km/h observes at noon a cuiser travelling due north at 20km/h. If the destroyer overtakes the cruiser one hour later find the distance and bearing of the cruiser from the destroyer at...
17. ### Find the velocity of the wind relative to the boat

Could someone please help me see where I am going wrong here? During a race between two boats A and B there is a wind of 18 km/h blowing from due north. The resultant velocity if A is 12 km/h on a bearing of 060. Find the direction of the wind relative to A. My reasoning: (Relative to the...
18. ### To find the amplitude of a mass on an elastic string

Could I please ask for help with the following: It's the final part I am having problems with. So at this point we know we have SHM of amplitude (5/4)L Now, using x = a cos(nt) ----- where we now know that n = sqrt(4g/L) we can find the time at which x has any value. So for exmaple, when...
19. ### To find the work done in extending a spring

Hi, Could I please ask where I am going wrong with this very simple question: Here's my answer (units implied): A force of 20 extends the spring by 1/100 and so the Work Done in performing this extension is 20 * 1/100 = 1/ 5 Now, the work done in extending a spring is given by the formula...
20. ### Find the height to which a mass rises

Hi, Could I please ask for help regarding the following question. The book answer H = ( 3 - 3 sqrt(2)/4 ) L (natural length of string is L) Here is my diagram: The green level represents the unstretched string. The blue level is the string and mass in equilibrium. The purple level is the...
21. ### Analysis of SHM of a mass

Could I please ask for views on this question: I've answered the whole thing and agree with the answers given in the text book. Here are those answers (where Y is the modulus of elasticity of the string = lamda in the question): Period of motion = 2 * PI * sqrt( ma/Y ) Speed passing...
22. ### To find the equilibrium position of a mass attached to an elastic string

Hi, can anyone see if I have made an error in answering this simple question, my answer is not the one given in the textbook. Here's my diagram of the system in equilibrium. So the mass has dropped a distance x below the midpoint of PQ: So the forces balance as: T1 = g + T2 So, using...
23. ### Travel time of a particle suspended from an elastic string

Hi, Can anyone please help me with the following: I have found the velocity of projection, no problem, it is v = 2*sqrt(10) Also, in obtaining this value, I have also found the extension in the string when in equilibrium, it is x = 2 Now on to the time of flight. The given answer is: t =...
24. ### To find the velocity of a mass attached to the midpoint of a spring

Could I please ask for help regarding part (a) of this question: If I get part (a) then part (b) will follow. So, here's my answer to part (a): I'll be using the formula Elastic Potential Energy in a spring = (Yx^2)/(2a) Where Y is the modulus of the spring, x the extension and a the natural...
25. ### Acceleration and Displacement from a Velocity vs. Time Graph

Please could I ask for help with the following question: Part (a) is no problem. Acceleration is the gradient of the graph in regions OA and AB which gives 3 and 0.5 Part (b), I believe, requires me to calculate the greatest and least value of the gradient of the curve in region BC Part...
26. ### Determination of the velocity of a particle in a hollow cone

Hi, please could I ask for help with the following question: A smooth hollow circular cone of semi-angle α, is fixed with its axis vertical and its vertex A downwards. A particle P, of mass m, moving with constant speed V, decribes a horizontal circle on the inner surface of the cone in a plane...
27. ### Calculation of minimum angular velocity of a mass on a spinning plate

Problem Statement: How to calculate minumum angular velocity of a mass on a spinning plate Relevant Equations: f=mrw^2 Hi, here's the question: a) A rough horizontal plate rotates with a constant angular velocity of w about a fixed vertical axis. A particle of mass m lies on the plate at a...
28. ### On the motion of a particle on the inner surface of a sphere

Could anyone please help me out with the second part of this question: I've got the first part, u = √(5ga) Here's my diagram for the second part: Distance travelled is from bottom of sphere to peg is 2πa/3 which means angle travelled is 2π/3. So the particale is going to travel 2π/3...