Work Energy And Power

Q: When a rubber-band is stretched by a distance x , it exerts a restoring force of magnitude F = ax + bx^2 where a and b are constants. The work done in stretching the unstretched rubber band by L is

F = ax + bx^2 dw = Fdx W = \displaystyle \int_0^L (ax + bx^2) dx W = \displaystyle \frac{aL^2}{2} + \frac{bL^3}{3}

Q: A body of mass starts moving from rest along x-axis so that its velocity varies as v = a\sqrt {s} where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first seconds after the start of the motion is:

Velocity of body v = a \sqrt s acceleration a' = \dfrac{dv}{dt} = \dfrac{a}{2 \sqrt s} \dfrac{ds}{dt} = \dfrac{a^2}{2} displacement s' = \dfrac{1}{2} a' t^2 = \dfrac{1}{2} \dfrac{a^2}{2} t^2 Work done W = force \times displacement W = ma' \times s' = \dfrac{1}{8} ma^4 t^2

Question

When a rubber-band is stretched by a distance $x$ , it exerts a restoring force of magnitude $F = a x + b x^{2}$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber band by $L$ is

Work Energy And Power

Physics
230 Views

When a rubber-band is stretched by a distance $x$ , it exerts a restoring force of magnitude $F = a x + b x^{2}$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber band by $L$ is

A body of mass starts moving from rest along x-axis so that its velocity varies as $v = a s$ where $a$ is a constant and $s$ is the distance covered by the body. The total work done by all the forces acting on the body in the first seconds after the start of the motion is:

Work Energy And Power

Physics 230 Views

When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude F=ax+bx2 where a and b are constants. The work done in stretching the unstretched rubber band by L is

A body of mass starts moving from rest along x-axis so that its velocity varies as v=as​ where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first seconds after the start of the motion is:

Physics
230 Views

When a rubber-band is stretched by a distance $x$ , it exerts a restoring force of magnitude $F = a x + b x^{2}$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber band by $L$ is

A body of mass starts moving from rest along x-axis so that its velocity varies as $v = a s$ where $a$ is a constant and $s$ is the distance covered by the body. The total work done by all the forces acting on the body in the first seconds after the start of the motion is: