Work, Energy and Power

A 0.5kg block moving at a speed of 12ms1 compresses a spring through a distance 30cm when its speed is halved. The spring constant of the spring will be…………Nm1.

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Contributor-Level 9

by conservation of mechanical energy

K.E_i + P.E_i = K.E_f + P.E_f

$\frac{1}{2} * 0.5 v^{2} + 0 = \frac{1}{2} * 0.5 {(\frac{v}{2})}^{2} + \frac{1}{2} k x^{2}$

$\Rightarrow \frac{1}{2} * 0.5 [v^{2} - \frac{v^{2}}{4}] = \frac{1}{2} k x^{2}$

$\Rightarrow \frac{1.5}{4} 12 * 12 = \frac{k * 9}{100}$

$\frac{1.5 * 36}{9} * 100 = k$

k = 600 N/m¹

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New answer posted

3 weeks ago

A particle moves with a velocity v = (5i - 3j + 6k) ms^-1 under the influence of a constant force F = (i - j - k)N. The instantaneous power applied to the particle is ______ Watts.

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Vishal Baghel

Contributor-Level 10

P = F.v = 5+3-6 = 2W

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3 weeks ago

A ball of mass 0.15 kg is dropped from a height. 10 m, strikes the ground and rehounds to the same height. The magnitude of impulse imparted to the ball is (g = 10 m/s² ) nearly:

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Contributor-Level 10

Velocity just before striking the ground
v? = √2gh
v? = √ (2*10*10) = 10√2 m/s
v? = -10√2?
If it reaches the same height, speed remains same after collision only the direction changes.
v? = 10√2 m/s
v? = 10√2?
|Impulse| = m|Δv|
= m|10√2? - (-10√2? )|
= 0.15 [2 (10√2)]
= 3√2 kg m/s
= 4.2 kg m/s

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3 weeks ago

A bullet from a gun is fired on a rectangular wooden block with velocity $u$ . When bullet travels 24cm through the block along its length horizontally, velocity of bullet become $\frac{u}{3}$ . Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:

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Contributor-Level 9

$\frac{1}{2} m {(\frac{u}{3})}^{2} - \frac{1}{2} {m u}^{2} = - F_{R} * 24$

$0 - \frac{1}{2} {m u}^{2} = - F_{R} * d$

$\frac{\frac{1}{2} {m u}^{2}}{\frac{1}{2} m u^{2} * \frac{8}{9}} = \frac{d}{24}$

$d = 24 * \frac{9}{8} = 27 c m$

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4 weeks ago

The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm , potential energy stored in it will be:

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Contributor-Level 9

Potential energy stored in the spring $= \frac{1}{2} {k x}^{2}$

$\begin{array}{r} Now \frac{1}{2} k (2)^{2} = U \\ & \frac{1}{2} k (8)^{2} = U^{'} (say) \\ \Rightarrow U^{'} = \frac{64}{4} U = 16 U \end{array}$

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4 weeks ago

Water falls from a height of $\frac{1}{3} {n m v}^{- 2}$ at the rate of $\sqrt[]{\frac{3 R T}{M}}$ to operate a turbine. The losses due to frictional force are $\frac{5}{2} R T$ of the input energy. How-much power is generated by the turbine? $\frac{3}{2} k_{B} T$ )

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Contributor-Level 10

$P_{in} = \frac{m g h}{t} = \frac{15 * 10 * 60}{1} = 9000 w$

$P_{out} = 90 %$ of $P_{in}$

$\Rightarrow 8.1 k w$

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4 weeks ago

A particle is released from height $S$ from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectively:

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Contributor-Level 10

$U + K E = E$

$4 U = E = m g S$

$4 m g h = m g S$

$h = \frac{S}{4}$

$v = \sqrt[]{2 g (\frac{3 S}{4})} = \sqrt[]{\frac{3 g S}{2}}$

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New answer posted

4 weeks ago

A bullet from a gun is fired on a rectangular wooden block with velocity $u$ . When bullet travels $24 c m$ through the block along its length horizontally, velocity of bullet become $\frac{u}{3}$ . Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:

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Contributor-Level 10

$i_{series} = \frac{E}{R_{series}}$

$\Rightarrow i_{series} = \frac{E}{10 R}$

$i_{parallel} = \frac{E}{R_{Parallel}}$

$= \frac{E}{R / 10}$ $i_{parallel} = n * i_{series}$

$\Rightarrow \frac{10 E}{R} = \frac{n E}{10 R}$

$\Rightarrow n = 100$

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4 weeks ago

An electric lift with a maximum load of 2000Kg (lift + passenger) is moving up with a constant speed $1.5 {m s}^{- 1}$ $^{}$ . The frictional force opposing the motion is 2000N $^{}$ . The minimum power delivered by the motor to lift in watts is : $(g = 10 {m s}^{- 2})$

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Contributor-Level 9

$\Rightarrow T = W + f$

$= 20000 + 3000$

$= 23000 N$

$\Rightarrow$ Power $= T v$

$= 23000 * 1.5$

$= 34500$ watts

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New answer posted

a month ago

The potential energy of a long spring when stretched by $2 c m$ is $U$ . If the spring is stretched by $8 c m$ , potential energy stored in it will be:

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