A block of mass m moving with a velocity v_0 | vedclass

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

Question

(B) For observer $A$ (ground frame),the block moves by a distance $x$ until it comes to rest.The force exerted by the spring on the block is $F = -kx$

Vedclass · Accepted Answer

$ - \frac{1}{2}mv_0^2$

Vedclass · Answer

(B) For observer $A$ (ground frame),the block moves by a distance $x$ until it comes to rest.The force exerted by the spring on the block is $F = -kx$ (in the opposite direction of motion).The work done by the spring force on the block is $W = \int_{0}^{x} (-kx) dx = -\frac{1}{2}kx^2$.According to the work-energy theorem,the total work done on the block is equal to the change in its kinetic energy.$W_{net} = \Delta K = K_f - K_i = 0 - \frac{1}{2}mv_0^2 = -\frac{1}{2}mv_0^2$.Since the surface is smooth and there is no other horizontal force,the work done by the normal reaction $N$ of the spring is the only work done on the block.Therefore,the work done by the normal reaction $N$ is $-\frac{1}{2}mv_0^2$.

Similar Questions

$A$ body of $0.5 \,kg$ moves along the positive $X$-axis under the influence of a varying force $F$ (in newton) as shown below. If the speed of the object at $x=4 \,m$ is $3.16 \,ms^{-1}$,then its speed at $x=8 \,m$ is ................. $\,ms^{-1}$.

The relationship between the force $F$ and position $x$ of a body is as shown in the figure. The work done in displacing the body from $x = 1 \text{ m}$ to $x = 5 \text{ m}$ will be ........ $J$.

$A$ particle is projected with velocity $v_{0}$ along the $x-$axis. $A$ damping force is acting on the particle which is proportional to the square of the distance from the origin,i.e.,$ma = -\alpha x^{2}$. The distance at which the particle stops is:

The work done by a force $\vec{F} = -5x^4 \hat{i} \text{ N}$ in displacing a body from $x = 2 \text{ m}$ to $x = -2 \text{ m}$ is: (in $\text{ J}$)

The potential energy $U(x)$ of a system is represented in the figure. The force $F(x)$ acting on the system will be represented by:

Vedclass Test Series

Exam Paper Generator

Online Exam Module