PHE-01/BPHE-101 Solved Assignment 2018

Description

PHE-01/BPHE-101 Solved Assignment 2018
Course Name: ELEMENTARY MECHANICS
Assignment Code: BPHE-101/PHE-01/TMA/2018
Medium: English
Valid From 1st January 2018 to 31st December 2018

Questions:

1. A crate of mass 30.0 kg is pulled by a force of 1800 N up an inclined plane which makes an angle of 30º with the horizon. The coefficient of kinetic friction between the plane and the crate is µ_k = 0.225. If the crates starts from rest, calculate its speed after it has been pulled 15.0 m. Draw the free body diagram.
2. A ball having a mass of 0.5 kg is moving towards the east with a speed of 8.0 ms^-1. After being hit by a bat it changes its direction and starts moving towards the north with a speed of 6.0 ms⁻¹. If the time of impact is 0.1 s, calculate the impulse and average force acting on the ball.
3. A box of mass 8.0 kg slides at a speed of 10 ms⁻¹ across a smooth level floor before it encounters a rough patch of length 3.0 m. The frictional force on the box due to this part of the floor is 70 N. What is the speed of the box when it leaves this rough surface? What length of the rough surface would bring the box completely to rest?
4. A wheel 2.0 m in diameter lies in the vertical plane and rotates about its central axis with a constant angular acceleration of 4.0 rad s⁻². The wheel starts at rest at t = 0 and the radius vector of a point A on the wheel makes an angle of 60º with the horizontal at this instant. Calculate the angular speed of the wheel, the angular position of the point A and the total acceleration at t = 2.0s.
5. A horizontal rod with a mass of 10 kg and length 12 m is hinged to a wall at one end
   and supported by a cable which makes an angle of 30º with the rod at its other end. Calculate the tension in the cable and the force exerted by the hinge.
6. A girl is sitting with her dog at the left end of a boat of length 10.0 m. The mass of the girl, her dog and the boat are 60.0 kg, 30.0 kg and 100.0 kg respectively. The boat is at rest in the middle of the lake. Calculate the center of mass of the system. If the dog moves to the other end of the boat, the girl staying at the same place, how far and in what direction does the boat move?
7. A child of mass 50 kg is standing on the edge of a merry go round of mass 250 kg and radius 3.0 m which is rotating with an angular velocity of 3.0 rad s⁻¹. The child then starts walking towards the centre of the merry go round. What will be the final angular velocity of the merry go round when the child reaches the centre?
8. At a crossing a truck traveling towards the north collides with a car travelling towards the east. After the collision the car and the truck stick together and move off at an angle of 30 º east of north. If the speed of the car before the collision was 20 ms⁻¹, and the mass of the truck is twice the mass of the car, calculate the speed of the truck before and after the collision.
9. Titan, a satellite of Saturn, has a mean orbital radius of 1.22 × 109 m. The orbital period of Titan is 15.95 days. Hyperion, another satellite of Saturn, orbits at a mean radius of 1.48 × 109 m. Estimate the orbital period of Hyperion.
10. a) What should be the angular velocity of the earth such that a person of mass 80 kg standing on the earth at the equator would actually fly off the earth?
    b) A ball of mass 60g is moving due south with a speed of 50 ms⁻¹ at latitude 30ºN. Calculate the magnitude and direction of the coriolis force on the ball. Compare the magnitude of this force to the weight of the ball.