All Solved Numerical of Chapter 4

All Solved Numerical of Chapter 4 

1. A car mechanic applies a force of 800 N to a wrench for the purpose of loosening a bolt. He applies the force which is perpendicular to the arm of the wrench. The distance from the bolt to the mechanic’s hand is 0.40 m. Find out the magnitude of the torque applied?

(320 N .m)

 

2. A car accelerates uniformly from rest and reaches a speed of 22 mIs in 9 s If the diameter of a tire is 58 cm, find

(a) the number of revolutions the tire makes during this motion, assuming no slipping, and

(b) the final rotational speed of the tire in revolutions per second.

 (55 rev, 12 rad /s)

 

 

3. An ordinary workshop grindstone has a radius of 7.5 cm and rotates 6500 rev/mm.

(a) Calculate the magnitude of centripetal acceleration at its edge in tns2 and convert it into multiples of g.

(b) What is the linear speed of a point on its edge?

(3.47xl0⁴m/s², 3.55xl0³g, 51 m/s)

 

4. A satellite is orbiting the Earth with an orbital velocity of 3200 m/s. What is the orbital radius? 

(3.897 x 10⁷ m)

 

 

5. A satellite wishes to orbit the earth at a height of 100 km (approximately 60 miles) above the surface of the earth. Determine the speed, acceleration and orbital period of the satellite. (Given: m_earth =5.98 x 10²⁴ kg, R_earth = 6.37 x l0⁶ m) 

(7.85x 10³ m/s, 9.53 m/s², 1.44 hours)

 

 

6. A thin disk with a 0.3m diameter and a total moment of inertia of  0.45 kg.m² is rotating about its center of mass. There are three rocks with masses of 0.2kg on the outer part of the disk. Find the total moment of inertia of the system. 

(0.464kg.m²)

 

 

7. What is the ideal banking angle for a gentle turn of 1.20 km radius on a highway with a

105 km/h speed limit (about 65 mi/h), assuming everyone travels at the limit?

 (4.14 degree)

 

8. A 1 500-kg car moving on a flat, horizontal road negotiates a curve as shown in Figure 4.21. If the radius of the curve is 35.0 m and the coefficient of static friction between the tires and dry

Pavement is 0.523, find the maximum speed the car can have  and still make the turn successfully

 (13.5 m/s)

 9.A system of points shown in figure 4.22. Each particle has same mass of 0.3 kg and they all lie in the same plane. What is the moment ot inertia of the system about given axis?

(0.13 kg m²)

10. (a) What is the angular momentum of a 2.9 kg uniform cylindrical grinding wheel of radius 20 cm when rotating 1550 rpm? (b) how much torque is required to stop it in 6 s ?

(9.5 kg.m²/s², - 1.6 N.m)

 

11. Determine the angular momentum of the Earth (a) about its rotation axis (Assume the

Earth as uniform sphere). and (b) in its orbit around the Sun (Take Earth as a particle

orbiting the Sun). The Earth has mass 6 x 10²⁴ kg and radius 6.4 x l0⁶m. and is 1.5 x l0⁸ km from the Sun.

 (7.3 x 10³³ kg.m²/s, 2.7 x 10⁴⁰ kg m²/s)