Kinetic energy, the work-energy theorem and power — practice questions

Question 1 · difficulty L2 · understanding

A block of mass $$5 \mathrm{~kg}$$ starting from rest pulled up on a smooth incline plane making an angle of $$30^{\circ}$$ with horizontal with an affective acceleration of $$1 \mathrm{~ms}^{-2}$$. The power delivered by the pulling force at $$t=10 \mathrm{~s}$$ from the start is ___________ W. [use $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$ ] (calculate the nearest integer value)

Question 2 · difficulty L2 · understanding

If the maximum load carried by an elevator is $$1400 \mathrm{~kg}$$ ( $$600 \mathrm{~kg}$$ - Passengers + 800 $$\mathrm{kg}$$ - elevator), which is moving up with a uniform speed of $$3 \mathrm{~m} \mathrm{~s}^{-1}$$ and the frictional force acting on it is $$2000 \mathrm{~N}$$, then the maximum power used by the motor is __________ $$\mathrm{kW}\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$$

Question 3 · difficulty L3 · understanding

A body of mass 2 kg begins to move under the influence of time dependent force $\overrightarrow{\mathrm{F}}=\left(2 \mathrm{t} \hat{\mathrm{i}}+6 \mathrm{t}^2 \hat{\mathrm{j}}\right) \mathrm{N}$, where $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ are unit vectors along $x$ and y -axis respectively. The power produced by the force at $t=2 \mathrm{~s}$ is $\_\_\_\_$ W.

Question 4 · difficulty L3 · understanding

A body of mass $2 \mathrm{~kg}$ is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in $4 \mathrm{~s}$ is $\frac{1}{3} \alpha^{2} \sqrt{P} m$. The value of $\alpha$ will be ______.

Question 5 · difficulty L3 · understanding

A body of mass 1kg begins to move under the action of a time dependent force $$\overrightarrow F = \left( {t\widehat i + 3{t^2}\,\widehat j} \right)$$ N, where $$\widehat i$$ and $$\widehat j$$ are the unit vectors along $$x$$ and $$y$$ axis. The power developed by above force, at the time t = 2s, will be ____________ W.

Question 6 · difficulty L3 · understanding

An object of mass 1000 g experiences a time dependent force $\vec{F}=\left(2 t \hat{i}+3 t^2 \hat{j}\right) N$. The power generated by the force at time $t$ is:

• A. $\left(2 t^2+18 t^3\right) W$
• B. $\left(3 t^3+5 t^5\right) w$
• C. $\left(2 t^3+3 t^5\right) w$
• D. $\left(2 t^2+3 t^3\right) w$

Question 7 · difficulty L3 · understanding

A sand dropper drops sand of mass m(t) on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e., $\frac{dm}{dt} \propto \sqrt{v}$. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

• A. P $\propto \sqrt{v}$
• B. P $\propto v$
• C. $P^2 \propto v^3$
• D. $P^2 \propto v^5$

Question 8 · difficulty L3 · understanding

A body of mass 4 kg is placed on a plane at a point $P$ having coordinate $(3,4) \mathrm{m}$. Under the action of force $\overrightarrow{\mathrm{F}}=(2 \hat{i}+3 \hat{j}) \mathrm{N}$, it moves to a new point Q having coordinates $(6,10) \mathrm{m}$ in 4 sec . The average power and instanteous power at the end of 4 sec are in the ratio of :

• A. 4 : 3
• B. 13 : 6
• C. 1 : 2
• D. 6 : 13

Question 9 · difficulty L3 · understanding

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to :

• A. t 2/3
• B. t 3/2
• C. t
• D. t 2

Question 10 · difficulty L3 · understanding

A body of mass $$2 \mathrm{~kg}$$ begins to move under the action of a time dependent force given by $$\vec{F}=\left(6 t \hat{i}+6 t^2 \hat{j}\right) N$$. The power developed by the force at the time $$t$$ is given by:

• A. $$\left(3 t^3+6 t^5\right) W$$
• B. $$\left(9 t^5+6 t^3\right) W$$
• C. $$\left(6 t^4+9 t^5\right) W$$
• D. $$\left(9 t^3+6 t^5\right) W$$