Work by Multiple Forces

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

1. $1.5\text{J}$
2. $3.6\text{J}$
3. $3\text{J}$
4. $4.5\text{J}$

Q. In a simple pendulum, work done by tension is non zero.

1. False
2. True

Q. A spring is fixed at the bottom end of an incline of inclination ${37}^{\circ }$. A small block of mass $2\text{kg}$ starts slipping down the incline from a point $4.8\text{m}$ away (along the inclined plane) from the spring. The block compresses the spring by $20\text{cm}$, stops momentarily and then rebounds through a distance of $1\text{m}$ up the incline. Then:

1. Friction co-efficient between the plane and block is $0.7$
2. Friction co-efficient between the plane and block is $0.5$
3. Spring constant is $1000\text{N/m}$
4. Spring constant is $800\text{N/m}$

Q. A body of mass m kg is lifted by a man to a height of one metre in 30 sec. Another man lifts the same mass to the same height in 60 sec. The work done by them(approximately) are in the ratio

1. 1 : 2
2. 1 : 1
3. 2 : 1
4. 4 : 1

Q. Three forces act on block as shown in figure.

Find work done by net force, if the block moves $10\text{m}$ in horizontal direction
Given magnitudes of forces are
[$F_1=20\text{N},F_2=5\sqrt{2}\text{N},F_3=10\text{N}$]

1. $50\text{J}$
2. $100\text{J}$
3. $75\text{J}$
4. Work done is equal to zero as there is no friction.

Q. Three forces are acting on the block as shown in figure.


Find work done by net force if block moves $10\text{m}$ in horizontal direction. Given that $[F_1=20\text{N},F_2=5\sqrt{2}\text{N},F_3=10\text{N}]$

1. $50\text{J}$
2. $100\text{J}$
3. $75\text{J}$
4. $\text{No work done as friction is absent}$

Q.

Multiple constant forces $F_1,......F_i$ are acting on an object of mass 'm' and produce a displacement S, with an acceleration a. Which of the following statements is true.

1. Work done on the object is ${\sum }_{i=1}^n\overrightarrow{F_i}.\overrightarrow{S}$

2. Work done on the object is $\left({\sum }_{i=1}^n\overrightarrow{F_i}\right).\overrightarrow{S}$

3. Work done on the object is $m\overrightarrow{a}.\overrightarrow{S}$

4. If all the forces are acting in the same direction, then work done will be maximum

Q. A constant force $\overrightarrow{F_1}=(2\hat{i}-4\hat{j})\text{N}$ displaces a particle from $(1,-1,2)$ to $(-1,-1,3)$ and then another force of $\overrightarrow{F_2}=(3\hat{i}+4\hat{j})\text{N}$, displaces it from $(-1,-1,3)$ to $(5,5,5)$ (displacements being measure in metre). Find the total work done.

1. $46\text{J}$
2. $38\text{J}$
3. $40\text{J}$
4. $36\text{J}$

Q. In the arrangement shown, the block is released from rest from $x=0$ (when the spring was in its natural length), on a rough incline surface having $\mu =0.5x.$ The maximum elongation in the spring will be,

1. $2\text{m}$
2. $2.5\text{m}$
3. $1\text{m}$
4. $1.5\text{m}$

Q. A particle is shifted from point $(0,0,1\text{m})$ to $(1\text{m},1\text{m},2\text{m})$, under the simultaneous action of several forces. Two of the forces are $\overrightarrow{F_1}=(2\hat{i}+3\hat{j}-\hat{k})\text{N}$ and $\overrightarrow{F_2}=(\hat{i}-2\hat{j}+2\hat{k})\text{N}$. Find the work done by these two forces

1. $7\text{J}$
2. $5\text{J}$
3. $10\text{J}$
4. $12\text{J}$

Q. The total work done by three forces on a block is $60\text{J}$. If block is displaced by a force from position $A(1,2,3)$ to $B(7,6,5)$. Find out the third force if the other two forces are $\overrightarrow{F_1}=(7\hat{i}+3\hat{j}+2\hat{k})\text{N}$, and $\overrightarrow{F_2}=(-2\hat{i}+2\hat{j}+\hat{k})\text{N}$.
Assume that $\overrightarrow{F_3}$ is perpendicular to $XY$ plane.

1. $\overrightarrow{F_3}=\hat{k}$
2. $\overrightarrow{F_3}=2\hat{k}$
3. $\overrightarrow{F_3}=3\hat{k}$
4. $\overrightarrow{F_3}=4\hat{k}$

Q. Three forces act on block as shown in figure.

Find work done by net force, if the block moves $10\text{m}$ in horizontal direction
Given magnitudes of forces are
[$F_1=20\text{N},F_2=5\sqrt{2}\text{N},F_3=10\text{N}$]

1. $50\text{J}$
2. $100\text{J}$
3. $75\text{J}$
4. Work done is equal to zero as there is no friction.