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Mechanics Questions from Mohammed

a. Determine the work done by the motor when the wheelchair starts at rest and speeds up to its normal speed.

b. Determine the maximum distance that the wheelchair can travel on a horizontal surface at its normal speed, using its stored energy. (Ignore the energy needed for it to speed up when it starts.)

c. Suppose that 0.023 percent of the power required for driving is expended against drag due to the flexing of the wheelchair’s soft rubber tires. Calculate the magnitude of the drag force.

Relative motion – Problem

A driving instructor tells his student to maintain a 3 second separation between the students car and the car ahead.

English: At The King Street Roundabout Traffic...

Suppose the cars are traveling 25m/s. How many meters apart are the cars? If the trailing car brakes at 9m/s^2 how much distance is required to stop?

(Received via SMS from the Mobile site of askphysics )

Get more such problems here and here

Answer:

a) 75 m

b)

Kinematics Problem

Three particles A,B,C are situated at vertices of a equilateral triangle ABC of side ‘a’ m at t=0 Each of the particle moves with constant speed ‘ v ‘. A always has it’s velocity along AB ,B always has it’s velocity along BC , C always has it’s velocity along CA. Derive the equation of trajectory of any one particle (means find y=f(x) i.e. relation between y and x coordinates of the particle). Also find the rate of rotation of the triangle formed by joining the lines connecting the three points as a function of time. If you think it requires more information such as acceleration etc., introduce them if needed.
Asked uppinder

Kinematics Problem

Three particles A,B,C are situated at vertices of a equilateral triangle ABC of side ‘a’ m at t=0 Each of the particle moves with constant speed ‘ v ‘. A always has it’s velocity along AB ,B always has it’s velocity along BC , C always has it’s velocity along CA. Derive the equation of trajectory of any one particle (means find y=f(x) i.e. relation between y and x coordinates of the particle). Also find the rate of rotation of the triangle formed by joining the lines connecting the three points as a function of time. If you think it requires more information such as acceleration etc., introduce them if needed.
Asked uppinder

Physics Numerical Problems posted by Nabeela

The following questions were posted by Nabeela. We are just posting the question as such so that the visitors can post the answers.

  1. A mass-less string pulls a mass of 20kg upward against gravity. The string would break if subjected to a tension greater than 400N. What is the maximum acceleration with which the mass can be moved upward?
  2. A bullet of mass 20g is fired from a gun of mass 10kg with a velocity of 180m/s. Find the velocity of recoil of the gun. Find the force required to stop the gun before it moves 20cm
  3. A free body diagram of a mass on an inclined planeA body of mass 40kg is moving up an inclined plane with a uniform velocity when a force of 460N is applied. If the plane is inclined to the horizontal by an angle of 45o,calculate the coefficient of kinetic friction between the surfaces.
  4. If the coefficient of friction between the tyres of a truck and the road is k, show that the maximum stopping distance of the truck when moving with a velocity ‘v’ is v2/2 kg. Assume that the brakes are not applied
  5. A ball of mass 0.5kg moving with a speed of 20m/s collides with an identical ball at rest. After collision the direction of each ball makes an angle of 30o with the original direction. Find the speed of each ball after collision.
  6. What is the maximum horizontal distance that a ball thrown with a speed of 60 m/s can go without hitting the roof of a long hall 30m high?
  7. A ball is thrown horizontally strikes a wall 5m away. The height of the point struck by the ball is 1m lower than the height which it was thrown from. (1) With what velocity was it thrown (2) At what angle did the ball reach the wall?
  8. The time of flight of aprojectile is 10 seconds . its range on a horizontal plane is 100m . Calculate the angle of projection and the velocity of projection.

Distance of closest approach of two ships problem

Two ships are 10 km apart on a line running south to north. The one farther north is steaming west at 20 km/h. The other is steaming north at 20 km/h. What is their distance of closest approach? How long do they take to reach it?

Asked Gayathri

Solution and Answer:

The main hindrance to solving problem is that students fail to visualize the situation.

Let’s represent the condition using a diagram.

Let the first ship steaming north be named A and the other B. The relative velocity of A with respect to B is 20 √2 south west.  If we extend the line along the 45° south west from the initial position of A, the distance of closest approach is the perpendicular drawn from B to this line.

So, the distance of closest appraoch = 10 sin 45° = 10/√2 = 7.07 m

Time taken to reach the distance of closest approach = distance of closest approach / relative speed

= (10/√2)/(20 √2)

= 0.25 h

Four persons K, L , M, N are initially at the four corners of a square of side d Problem

Four persons K, L , M, N are initially at the four corners of a square of side ‘d’. Each person now starts moving with a uniform speed ‘v’ in such a way that K always moves directly towards L, L towards M, M towards N and N towards K. After what time will they meet?

Gayathri asked.

Answer: Many students do not understand the real situation initially. Every time the persons are approaching each other and hence they will be moving closer and closer as they continue their walking. Finally they’ll reach the centre of the square to meet each other. I’ve tried to visualize the situation below.

From the diagram, we can make out that the resultant displacement by each when they meet will be d/√2 and the component of velocity of each towards the final point (the centre of the square) is v/√2.

Therefore,the time taken = displacement by the component of velocity in its direction = (d/√2) / (v/√2) = d/v

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