Laws Of Motion

Q: A uniform rod AB is suspended from a point X , at a variable distance x from A , as shown. To make the rod horizontal, a mass m is suspended from its end A . A set of (m,x) values is recorded. The appropriate variables that give a straight line, when plotted, are:

Let, 'l' and 'M' be the length and mass of rod.for equilibrium, taking moment about X, we get m \times x = M \times (\dfrac{l}{2} - x) this can be written as, m = (\dfrac{Ml}{2}) \dfrac{1}{x} - M comparing with straight line equation, y = mx + cwe can say that, m \propto \dfrac{1}{x}

Q: Two identical ladders are arranged as shown in the figure. Mass of each ladder is M and length L . The system is in equilibrium. Find direction and magnitude of friction force acting at A or B.

Drawing the FBD of both rods As the rods are in equilibrium \Sigma F_{X}=0 \Sigma F_{y}=0 \tau_{\mathrm{n}\mathrm{e}\mathrm{t}}=0 For right rod N_{2}+\displaystyle \frac{mg}{2}+Mg=N (1) N_{1}=f (2)For left rod N_{2}+N=Mg+\displaystyle \frac{mg}{2} (3)From (1)\mathrm{a}\mathrm{n}\mathrm{d}(3)N_{1}=f = N_{2}=0 = N=Mg+\displaystyle \frac{mg}{2} Balancing torque about \mathrm{O} , Mg\displaystyle \frac{L}{2}\cos\theta +fL \sin\theta =NL\cos\theta \displaystyle \frac{Mg\cos\theta}{2}+f\sin\theta =(Mg+\displaystyle \frac{mg}{2})\cos\theta f=(\displaystyle \frac{Mg}{2}+\frac{mg}{2})\cot\theta = f=(\displaystyle \frac{M+m}{2})g\cot\theta

Question

A uniform rod $A B$ is suspended from a point $X$ , at a variable distance $x$ from $A$ , as shown. To make the rod horizontal, a mass $m$ is suspended from its end $A$ . A set of $(m, x)$ values is recorded. The appropriate variables that give a straight line, when plotted, are:

Laws Of Motion

Physics
354 Views

A uniform rod $A B$ is suspended from a point $X$ , at a variable distance $x$ from $A$ , as shown. To make the rod horizontal, a mass $m$ is suspended from its end $A$ . A set of $(m, x)$ values is recorded. The appropriate variables that give a straight line, when plotted, are:

Two identical ladders are arranged as shown in the figure. Mass of each ladder is $M$ and length $L$ . The system is in equilibrium. Find direction and magnitude of friction force acting at A or B.

Laws Of Motion

Physics 354 Views

A uniform rod AB is suspended from a point X, at a variable distance x from A, as shown. To make the rod horizontal, a mass m is suspended from its end A. A set of (m,x) values is recorded. The appropriate variables that give a straight line, when plotted, are:

Two identical ladders are arranged as shown in the figure. Mass of each ladder is M and length L. The system is in equilibrium. Find direction and magnitude of friction force acting at A or B.

Physics
354 Views

A uniform rod $A B$ is suspended from a point $X$ , at a variable distance $x$ from $A$ , as shown. To make the rod horizontal, a mass $m$ is suspended from its end $A$ . A set of $(m, x)$ values is recorded. The appropriate variables that give a straight line, when plotted, are:

Two identical ladders are arranged as shown in the figure. Mass of each ladder is $M$ and length $L$ . The system is in equilibrium. Find direction and magnitude of friction force acting at A or B.