A block has an initial kinetic of $128\mathrm{J}.$ It slides up from point $A$ at the bottom of the inclined plane with uniform deceleration. when it passes point $B,$ its kinetic energy is reduced by $80\mathrm{J}$, and its mechanical energy is reduced by $35\mathrm{J}.$ Calculate the work done against friction when the block move from $A$ to the highest point $C$ on the inclined plane.

 

A cylindrical trough is placed on a horizontal plane. The two edge of the trough are connected with smooth inclined planes $AA\text{'}$ and $BB\text{'}$ at locations $A$ and $B$ respectively. The trough edges and the inclined planes are tangential at the connections, and $A,B$ are located at the same horizontal level, as shown in the figure. A small mass slides freely down the slope $A\text{'}A$ from a height of $2\mathrm{h}$ above the horizontal level $AB$. It enters the trough at position $A,$ reaches $B$ and then slides upward along slope $BB\text{'}$ until it reaches a height of $h$ above the horizontal level $AB$. It then slides downwards along slope $B\text{'}B$ and enters the trough again. Neglecting air resistance, the small mass

A small body slips, subject to the force of friction, from point $A$ to point $B$ along two curved surfaces of equal radius, first along route $1,$ then along route $2$. The coefficient of on both routes is the same.In which case will the body's speed at $B$ be greater?

A non-Hookian spring has force $F=-k{x}^2$, where $k$ is the spring constant and $x$ is the displacement from its unstretched position. For the system shown of mass $m$ connected to an unstretched spring initially at rest, how far does the spring extend before the system momentarily come to rest? Assume that all surfaces are frictionless and that the pulley is frictionless as well.

A massless string of length $2l$ connects two hockey pucks that lie on frictionless ice. A constant horizontal force $F$ is applied to the midpoint of the string, perpendicular to it (see figure). What is the kinetic energy of a puck just before the pucks collide.

In the figure shown the potential energy $\left(U\right)$ of a particle is plotted against its position '$x$' from origin. Then which of the following statement is correct. A particle at:

The teeter toy consists of two identical weights which hang form a peg on drooping arms as shown in the figure. The arrangement is unexpectedly stable. The toy can be spun or rocked with little danger of toppling over. For simplicity consider only rocking motion in the vertical plane. For the teeter toy to be stable

The given plot shown the variation, the potential energy $\left(U\right)$ of interaction between two particle with the separating distance $\left(r\right)$ between them. Which of the above statements are correct?

(1) $B$ and $D$ are equilibrium points 

(2) $C$ is a point of stable equilibrium points 

(3) The force of interaction between the two particle is attractive between points $C$ and $D$ and repulsive between points between $D$ and $E$ on the curve.

(4) The force of interaction between the particles is repulsive between points $E$ and $F$ on the curve.