Work Done as Dot Product

Q. A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by F = −ˆi + 2 ˆj + 3 kˆ N where ˆi, ˆj, kˆ are unit vectors along the x-, y- and z-axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis ?

Q.

A cord is used to lower vertically a block of mass M by a distance d with constant downward acceleration $\frac{g}{4}$ . Work done by the cord on the block is

1. 

2. 

3. Mgd

4. 

Q.

The work done in pulling up a block of wood weighing 2 kN for a length of 10m on a smooth plane inclined at an angle of ${15}^{\circ }$ with the horizontal is

1. 5.17 kJ

2. 4.36 kJ

3. 8.91 kJ

4. 9.82 kJ

Q. The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative: (a) work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket. (b) work done by gravitational force in the above case, (c) work done by friction on a body sliding down an inclined plane, (d) work done by an applied force on a body moving on a rough horizontal plane with uniform velocity, (e) work done by the resistive force of air on a vibrating pendulum in bringing it to rest.

Q.

Is compressing a spring positive or negative work?

Q.

A particle of mass 0.01 kg travels along a curve with velocity given by $4\hat{i}+16\hat{k}m{s}^{-1}$. After some time, its velocity becomes $8\hat{i}+20\hat{j}m{s}^{-1}$due to the action of a conservative force. The work done on particle during this interval of time is

1. 6.9 J

2. 0.32 J

3. 9.6 J

4. 0.96 J

Q.

A force of 5 N acts on a 15 kg body initially at rest. The work done by the force during the first second of motion of the body is

1. 5 J

2. 

3. 6 J

4. 

Q.

The mass of a bucket containing water is 10 kg. What is the work done in pulling up the bucket from a well of depth 10 m if water is pouring out at a uniform rate from a hole in it and there is loss of 2kg of water from it while it reaches the top $(g=10m/se{c}^2)$

1. 900 J

2. 500 J

3. 1000 J

4. 800 J

Q.

Find the value of m so that the vector 3$\hat{i}-2\hat{j}+\hat{k}$ may be perpendicular to the vector $2\hat{i}+6\hat{j}+m\hat{k}$.

1. m = 2

2. m = 3

3. m = 5

4. m = 6

Q.

A small block of mass 2 kg is kept on a rough inclined surface of inclination $\theta ={30}^{\circ }$ fixed in a lift. The lift goes up with a uniform speed of 1 m$s^{-1}$ and the block does not slide relative to the inclined surface. The work done by the force of friction on the block in a time interval of 2 s is.

1. Zero

2. 9.8 J

3. 29.4 J

4. 16.9 J

Q.

State, whether the work done in the following cases, is positive or negative.

Work done by resistive force of air on a pendulum bob to bring it to rest.

Q. 42.A force F=5i+6j-4k acting on a body produces a displacement d=3i+2k work done by the force is

Q. A body of mass $25\text{kg}$ slides down a smooth incline as shown. Find the work done by force of gravity till the body reaches the bottom of the inclined plane ($g=10{\text{ms}}^{-2}$)

1. $0\text{J}$
2. $1125\text{J}$
3. $2250\text{J}$
4. $4500\text{J}$

Q.

The US athlete Florence Griffith - Joyner won the 100 m sprint gold medal at SeoulOlympic 1988 setting a new Olympic record of 10.54 s. Assume that she achieved her maximum speed in a very short-time and then ran the race with that speed till she crossed the line. Take her mass to be 50 kg. Assuming that the track, the wind etc. offered an average resistance of one tenth of her weight, calculate the work done by the resistance during the run.

1. 4900 J

2. -4900 J

3. Zero

4. 50 J

Q.

Does the work done in raising a box onto a platform depend on how fast is raised $?$

Q. A rod AB of mass 10kg and length 4m rests on a horizontal floor with end A fixed so as to rotate it in vertical plane about perpendicular axis passing through A. If the work done on the rod is 100J, the height to which the end B be raised vertically above the floor is [Kerala PET 2007] (a) 1.5 m (c) 1.0 m (b) 2.0 m (d) 2.5 m

Q.

A truck with mass m has a brake failure while going down an icy mountain road of constant downward slope angle α (see figure). Initially, the truck is moving downhill at speed v₀. After careening downhill a distance L with negligible friction, the truck driver steers the runaway vehicle onto a runaway truck ramp of constant upward slope angle β. The truck ramp has a soft sand surface for which the coefficient of rolling friction is μ_r. What is the distance that the truck moves up the ramp before coming to a halt?

1. $({v_0}^2/2g)+L\sin \alpha /\sin \beta +{\mu }_r\cos \beta$

2. $({v_0}^2/2g)-L\sin \alpha /\sin \beta +{\mu }_r\cos \beta$

3. $({v_0}^2/2g)+L\sin \alpha /\sin \beta -{\mu }_r\cos \beta$

4. None of these.

Q. A force $\overrightarrow{F}=6x\hat{i}+2y\hat{j}$ displaces a body from $\overrightarrow{r_1}=3\hat{i}+8\hat{j}$ to $\overrightarrow{r_2}=5\hat{i}-4\hat{j}$. Find the work done by the force.

1. $0\text{J}$
2. $75\text{J}$
3. $64\text{J}$
4. $16\text{J}$

Q. a person applies a force f on a box inside a moving train. If S1 is the displacement of box w.r.t. train and S2 is the displacement of train w.r.t. grounf, then the work done by the person in the frame of earth will be 1. F. S1 2. F.S2 3. F. (S1+S2) 4. F. (S1- S2)

Q. A body constrained to move in $z$ direction is subjected to a force given by $\overrightarrow{F}=(3\hat{i}-10\hat{j}+5\hat{k})\text{N}.$ What is the work done by this force in moving the body through a distance of $5\text{m}$ along $z-$axis?

1. $15\text{J}$
2. $15\text{J}$
3. $-50\text{J}$
4. $25\text{J}$

Q. A body of mass $3\text{kg}$ is under a constant force has displacement $s$, given by the relation $s=\frac{1}{3}{t}^2$, where $t$ is in seconds, $s$ is in metres. Work done by the force in $2$ seconds is

1. $\frac{19}{5}\text{J}$
2. $\frac{5}{19}\text{J}$
3. $\frac{3}{8}\text{J}$
4. $\frac{8}{3}\text{J}$

Q. Figure shows three forces applied to a trunk that moves leftward by $3$ m over a smooth floor. The force magnitudes are $F_1=5N,F_2=9N,$ and $F_3=3N$. The net work done on the trunk by the three forces

1. $1.50\text{J}$
2. $2.40\text{J}$
3. $3.00\text{J}$
4. $6.00\text{J}$

Q. A force $F=10+2y$ acts on a particle in $y$ - direction, where $F$ is in Newtons and $y$ is in metres. Work done by this force to move the particle from origin to $2\text{m}$ along $+y$ direction is

1. $24\text{J}$
2. $32\text{J}$
3. $48\text{J}$
4. $12\text{J}$

Q. A block of mass 1 kg is placed at point A of a rough track shown in figure (8-E6). If slightly pushed towards right, it stops at point B of the track. Calculate the work done by the frictional force on the block during its transit from A to B.
Figure

Q. A force $\overrightarrow{F}=(5\hat{i}+3\hat{j}+2\hat{k})\text{N}$ is applied over a particle which displaces it to a point having position vector$\overrightarrow{r}=(2\hat{i}-\hat{j})\text{m}$ from origin. The work done on the particle (in $\text{J}$) is

1. $+10$
2. $+7$
3. $-7$
4. $+13$

Q. A particle moves along the $x-$axis from $x=1\text{m}$ to $x=3\text{m}$ under the influence of a force $F=3x^2-2x+5$ newton acting along $x-$ axis. The work done in this process is

1. $9\text{J}$
2. $28\text{J}$
3. $27\text{J}$
4. zero

Q. A particle moves under the effect of a force $F=k{x}^2$. Find work done by force when particle displaces from $x=0\text{m}$ to $x=4\text{m}$.

1. $\frac{8k}{3}$
2. $\frac{32k}{3}$
3. $\frac{64k}{3}$
4. $\frac{128k}{3}$

Q. A force $\overrightarrow{F}=6x\hat{i}+2y\hat{j}$ displaces a body from $\overrightarrow{r_1}=3\hat{i}+8\hat{j}$ to $\overrightarrow{r_2}=5\hat{i}-4\hat{j}$. Find the work done by the force.

1. $0\text{J}$
2. $75\text{J}$
3. $64\text{J}$
4. $16\text{J}$

Q. Direction of force and displacement should always be same for a non zero work.

1. True
2. False

Q. Find the work done by tension (in $\text{J}$) on $1\text{kg}$ block when $4\text{kg}$ block moves down by $20\text{cm}$ after the system is released. All surfaces are frictionsless

1. $4\text{J}$
2. $6\text{J}$
3. $5\text{J}$
4. Zero