Work Done by Friction

Q. Consider the situation as shown in figure. A constant force acting on the lower blocks produces an acceleration of $4{\text{m/s}}^2.$ The two blocks always move together. Find the work done by static friction on the upper block during displacement $2\text{m}$ of the system.

1. $8\text{J}$
2. Zero
3. $16\text{J}$
4. $10\text{J}$

Q. If 250J of work is done in slidinga5kg blockup an inclined plane of height 4m. Work done agaist friction

Q.

A large slab of mass 5 kg lies on a smooth horizontal surface, with a block of mass 4 kg lying on the top of it. The coefficient of friction between the block and the slab is 0.25. if the block is pulled horizontally by a force of F = 6 N, the work done by the force of friction on the slab, between the instants t=2 s and t=3 s, is (g = 10 m$s^{-2}$)

1. 4.44 J

2. 10 J

3. 2.4 J

4. 5.55 J

Q.

Statement I: A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving a certain distance. The surface is now tilted to an angle of ${30}^{\circ }$ with the horizontal, and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.
Statement II: The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

1. If statement I is true, Statement II is true; Statement II is the correct explanation for Statement I

2. If statement I is true, Statement II is true; Statement II is not correct explanation for Statement I

3. If statement I is true, Statement II is false

4. If statement I is false, Statement II is true

Q.

A block of mass 5.0 kg slides down from the top of an inclined plane of length 3 m. The first 1 m of the plane is smooth and the next 2 m is rough. The block is released from rest and again comes to rest at the bottom of the plane. If the plane is inclined at ${30}^{\circ }$ with the horizontal, find the coefficient of friction on the rough portion.

1. $\frac{2}{\sqrt{3}}$

2. $\frac{\sqrt{3}}{2}$

3. $\frac{\sqrt{3}}{4}$

4. $\frac{\sqrt{3}}{5}$

Q. A body of mass $2\text{kg}$ initially at rest moves under the action of an applied horizontal force of $7\text{N}$ on a table with coefficient of kinetic friction ${\mu }_k=0.1$.
Calculate the work done by kinetic friction in $10\text{sec}(g=9.8{\text{m/s}}^2)$

1. $246.96\text{J}$
2. $-246.96\text{J}$
3. $882\text{J}$
4. $-882\text{J}$

Q. A block of mass $M$ is pulled along a horizontal surface by applying a force at an angle $\theta$ with the horizontal. The friction coefficient between the block and the surface is $\mu$. If the block travels at a uniform velocity, then the work done by this applied force during a displacement $d$ of the block is

1. $W=\frac{\mu Mgd\cos \theta }{\cos \theta +\mu \sin \theta }$
2. $W=\frac{\mu Mgd\cos \theta }{\sin \theta +\mu \cos \theta }$
3. $W=\frac{\mu Mgd\sin \theta }{\sin \theta +\mu \cos \theta }$
4. $W=\frac{\mu Mgd\sin \theta }{\sin \theta +\mu \cos \theta }$

Q. A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination ${30}^o$. The coefficient of static friction ${\mu }_s=0.25$.
(a) How much is the force of friction acting on the cylinder ?
(b) What is the work done against friction during rolling ?
(c) If the inclination $\theta$ of the plane is increased, at what value of $\theta$ does the cylinder begin to skid, and not roll perfectly ?

Q. A block of mass $5\text{kg}$ slides down on a rough inclined plane of coefficient of friction $0.75$ having angle of inclination ${37}^{\circ }$ as shown in the figure. Initially if the block is at rest on the top of inclined plane of length $2\text{m}$, then the work done against the friction in moving the block to the bottom of inclined plane is (Take $g=10{\text{m/s}}^2$).

1. $0\text{J}$
2. $5\text{J}$
3. $10\text{J}$
4. $-5\text{J}$

Q.

A block of mass 5.0 kg slides down from the top of an inclined plane of length 3 m. The first 1 m of the plane is smooth and the next 2 m is rough. The block is released from rest and again comes to rest at the bottom of the plane. If the plane is inclined at ${30}^{\circ }$ with the horizontal, find the coefficient of friction on the rough portion.

1. $\frac{2}{\sqrt{3}}$

2. $\frac{\sqrt{3}}{2}$

3. $\frac{\sqrt{3}}{4}$

4. $\frac{\sqrt{3}}{5}$

Q. In a figure shown below, the work done by force of friction on the block is

1. Zero
2. Positive
3. Negative
4. cannot be determined

Q. A car is moving on a circular track of radius $R$. The road is banked at $\theta .\mu$ is the coefficient of friction. Find the maximum speed the car can have.

1. ${\left[\frac{Rg(\sin \theta +\mu \cos \theta )}{\cos \theta +\mu \sin \theta }\right]}^{1/2}$
2. ${\left[\frac{Rg(\cos \theta +\mu \sin \theta )}{\cos \theta -\mu \sin \theta }\right]}^{1/2}$
3. ${\left[\frac{Rg(\sin \theta +\mu \cos \theta )}{\cos \theta -\mu \sin \theta }\right]}^{1/2}$
4. $None$

Q. Can the work by kinetic friction on an object be positive? Zero?

Q.

The work done by kinetic friction on an object is always negative.

1. True

2. False

Q. A $10\text{kg}$ block placed on a rough horizontal floor is being pulled by a constant force $F=100\text{N}$ acting at angle ${37}^{\circ }$. The coefficient of kinetic friction between the block and the floor is $0.4$. Find the total work done on the block over the displacement of $5\text{m}$.

1. $480\text{J}$
2. $360\text{J}$
3. $320\text{J}$
4. $400\text{J}$

Q. A block of mass $m$ is placed on an inclined plane which is moving with constant velocity $v$ in horizontal direction as shown in figure. Then find out work done in ground frame by the friction in time $t$, if the block is at rest with respect to the inclined plane.

1. $-mgvt\sin \theta \cos \theta$
2. $-mgvt{\cos }^2\theta$
3. $mgvt\sin \theta \cos \theta$
4. $-mgvt\sin \theta$

Q. A block of mass $1\text{kg}$ slides down on a rough inclined plane of inclination ${60}^{\circ }$ starting from its top. If the coefficient of kinetic friction is 0.5 and the length of the plane is $1\text{m}$, then work done against friction is (Take $g=9.8{\text{m/s}}^2$)

1. $9.82\text{J}$
2. $4.94\text{J}$
3. $2.45\text{J}$
4. $1.96\text{J}$

Q. A block of mass $10\text{kg}$ lies on a rough plane as shown in the figure. A constant force $F$ is applied for $10$ seconds, find out the value of work done by the force $F$.

1. $12000\text{J}$
2. $10000\text{J}$
3. $-6000\text{J}$
4. $0\text{J}$ (because friction is present)

Q. A block of mass $m$ is moving down with constant velocity along an inclined plane of inclination $\theta$. What is the work done by an external force (applied parallel to the inclined plane) in pulling the block up the inclined plane through a height ${}^{\prime }{h}^{\prime }$ with constant velocity?

1. $3mgh$
2. $mgh$
3. $mgh\sin \theta$
4. $2mgh$

Q. In the arrangement shown in figure $m_A=4.0\text{kg}$ and $m_B=1.0\text{kg}.$ The system is released from rest and block $B$ is found to have a speed $0.3\text{m/s}$ after it has descended through a distance of $1\text{m}$. Find the coefficient of friction between the block $A$ and the table. Neglect friction elsewhere. (Take $g=10m/s^2$)

1. $0.231$
2. $0.501$
3. $0.110$
4. $0.23$