An engine is attached to a wagon through a sh | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The initial kinetic energy of the system is $K_i = \frac{1}{2}mv^2$,where $m = 40,000\, 	ext{kg}$ and $v = 72\, 	ext{km/h} = 20\, 	ext{m/s}$.$K

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(A) The initial kinetic energy of the system is $K_i = \frac{1}{2}mv^2$,where $m = 40,000\, 	ext{kg}$ and $v = 72\, 	ext{km/h} = 20\, 	ext{m/s}$.$K_i = \frac{1}{2} 	imes 40,000 	imes (20)^2 = 80,00,000\, 	ext{J} = 80 	imes 10^5\, 	ext{J}$.According to the work-energy theorem,the total work done is equal to the change in kinetic energy: $W_{	ext{friction}} + W_{	ext{spring}} = K_f - K_i$.Given that $90\%$ of the energy is lost due to friction,$W_{	ext{friction}} = -0.9 K_i$.Since the system comes to rest,$K_f = 0$. Thus,$-0.9 K_i + W_{	ext{spring}} = -K_i$.$W_{	ext{spring}} = -0.1 K_i$.The work done by the spring is $W_{	ext{spring}} = -\frac{1}{2}kx^2$,where $x = 1.0\, 	ext{m}$.$-\frac{1}{2}k(1)^2 = -0.1 	imes (80 	imes 10^5)$.$\frac{1}{2}k = 8 	imes 10^5$.$k = 16 	imes 10^5\, 	ext{N/m}$.Therefore,the spring constant is $16 	imes 10^5\, 	ext{N/m}$.

Similar Questions

$A$ smooth sphere of mass $m$ moving with velocity $u$ collides with another smooth sphere of mass $2m$ at rest. What is the range of the velocity $v$ of the second sphere after the collision?

$A$ body of mass $4 \,kg$ is moving with momentum of $8 \,kg \,m/s$. $A$ force of $0.2 \,N$ acts on it in the direction of motion of the body for $10 \,s$. The increase in kinetic energy in joules is

$A$ rigid body of mass $4 \ kg$ initially at rest moves under the action of an applied horizontal force of $18 \ N$ on a table with a coefficient of kinetic friction of $0.2$. The work done by the applied force on the body in $10 \ s$ will be $.... \ J$.

If a shell fired from a cannon explodes in mid-air,then which of the following is true?

$A$ man throws a ball to a height of $12 \ m$,where it reaches with a speed of $12 \ m/s$. If the man throws the ball such that it just reaches this height,what percentage of energy would he have saved?

Vedclass Test Series

Exam Paper Generator

Online Exam Module