Question

12. A minimum force 5N is required to make a body of mass 2kg move on a horizontal floor. But a force 4N is required to maintain its motion with a uniform velocity. Calculate coefficient of static friction and coefficient of kinetic friction.
13. A box of mass 70 kg is pulled by a horizontal force of 500 N on the surface of the floor. When the box moves, the co-efficient of friction between the floor and the box is 0.50. Calculate the acceleration of the box.
14. The mass of metal sphere is 6g. it is rotated 4times per sec by fastening it at the end of a thread length 3m. What is its angular momentum?
15. A wheel weighing 5kg and radius of gyration about an axis is 0.2m. What is its moment of inertia? In order to produce angular acceleration of 2rad/s in the wheel. What magnitude of torque is to be applied?

Answer 1

Answer on Question # 83102, Physics / Quantum Mechanics

Question 1. A minimum force $5\,N$ is required to make a body of mass 2kg move on a horizontal floor. But a force $4\,N$ is required to maintain its motion with a uniform velocity. Calculate coefficient of static friction and coefficient of kinetic friction.

Solution 1. Coefficient of static friction is $\mu_{s}=F_{min}/mg=4/(2\cdot 10)=0.2.$ Coefficient of kinetic friction is $\mu_{k}=F/F_{N}=F/mg=5/(2\cdot 10)=0.25.$ $\square$

Question 2. A box of mass $70\,kg$ is pulled by a horizontal force of $500\,N$ on the surface of the floor. When the box moves, the co-efficient of friction between the floor and the box is $0.5$. Calculate the acceleration of the box.

Solution 2. $F-\mu mg=ma\Rightarrow a=F/m-\mu g=500/70-0.5\cdot 10=15/7\approx 2.143m/s^{2}.$ $\square$

Question 3. The mass of metal sphere is $6\,g$. it is rotated $4$ times per sec by fastening it at the end of a thread length $3\,m$. What is its angular momentum?

Solution 3. $\omega=2\pi f,$ $I=mr^{2}\Rightarrow L=I\omega=mr^{2}\cdot 2\pi f=6\cdot 10^{-3}\cdot 3^{2}\cdot 2\pi\cdot 4\approx 1.36\,m^{2}\cdot kg/s.$ $\square$

Question 4. A wheel weighing $5\,kg$ and radius of gyration about an axis is $0.2\,m$. What is its moment of inertia? In order to produce angular acceleration of $2\,rad/s^{2}$ in the wheel. What magnitude of torque is to be applied?

Solution 4. Moment of inertia is $I=mr^{2}=5\cdot 0.2=1\,kg\cdot m^{2}.$ Magnitude of torque is $M=I\frac{d\omega}{dt}=1\cdot 2=2\,N\cdot m.$ $\square$