## Numerical Problems on Vectors and Equilibrium

See here solution of numerical problems included in the First Year Physics Course.

** Problem 1:** A ship leaves a port P and travel 30 km due north. Then it changes course and travels 20 km in a direction 30^{0} east of north to reach port R. Calculate the distance from P to R.

**Problem 2:** A certain corner of the room is selected as origin of the rectangular coordinate system. If an insect is sitting on an adjacent wall at a point whose coordinates are (2, 1, 0) in units of meter, what is the distance of the insect from this corner of the room?

**Problem 3:** The magnitudes of the dot and cross product of two vectors are and 6 respectively. Find the angle between the vectors.

**Problem 4:** A load of 10.0 N is suspended by a clothes line (tanab). It distorts the line so that it makes an angle of 15^{0} with the horizontal at each end. Find the tension in the clothes line.

**Problem 5:** Four coplanar forces act on a body at a point O as shown in figure. Find their resultant.

**Problem 6:** A force of 5 N is applied perpendicular to the plane of a uniform door 2 m high and 0.6 m wide. Find the torque along the line joining the hinge. (Hinges mean the pivots or turning points of the door. QABZE in Pashto).

**Problem 7:** Find the magnitude of the forces provided by the supports A and B if shown a balanced condition. Weight of plank is 500 N and it is uniform in shape. Weight of the bloc= 100 N, Weight of the student = 500 N.

**Problem 8:** Three forces are acting on a body as shown. Find the magnitude of their resultant and also state in which plane the final resultant lies.

**Problem 9:** A meter rule is supported on a knife edge placed at the 40 cm graduation. It is found that the meter rule balances horizontally when a mass which has a weight of 0.45 N is suspended at the 15 cm graduation. As shown in the diagram.

(a) Calculate the moment about the knife edge in this balanced condition of the force due to the mass of the rule.

(b) If weight of the ruler is 0.90 N then find the position of its center o f gravity.

**Problem 10:** A uniform plank AB of length 4 m and weight 500 N is suspended by a vertical rope at each end. A girl of weight 300 N is standing at a distance of 1.2 m from the end A, calculate the tension in the rope supporting end B. Would you expect the tension in the rope at A to be larger or smaller than the rope at B. State a reason for your answer.

**Problem 11:** The diagram below shows the plan view of a door hinged at A. If a man applies a force F of 40 N at the end marked B, calculate the moment of this force about A. What is the minimum force X that must be applied at C in order to stop the door from turning? Name the principle applied to solve this problem.

**Problem 12:** Consider a ladder weighing 200 N resting against a smooth wall such that it makes an angle 60^{0} with the horizontal. Find the reactions on the ladder due to the wall and ground.

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