help@askiitians.com

+91-87964 74404

Grade 12Mechanics

A collar of mass m slides up the vertical shaft under the action of a force F of constant magnitude but variable direction. If θ = Kt, where K is a constant and if the collar starts from rest with θ = 0. Find the magnitude F of the force which will result in the collar coming to rest as θ reaches π/2. The coefficient of kinetic friction between collar and shaft is μ.

Question image for A collar of mass m slides up the vertical shaft u

Aslan

8 Years agoGrade 12

3 Answers

Eshan

8 Years ago

Net force acting on the body upwards= $Fcos\theta-mg-\mu (Fsin\theta)=ma$

$\implies \dfrac{dv}{dt}=\dfrac{Fcos\theta-mg-\mu (Fsin\theta)}{m}$
$=\dfrac{F}{m}(cos(Kt)-\mu sin(Kt))-g$
$\implies v=\int_0^{\pi/2}(\dfrac{F}{m}(cos(Kt)-\mu sin(Kt))-g)dt$
$\implies \int_0^0 dv=\int_0^{t_0}(\dfrac{F}{m}(cos(Kt)-\mu sin(Kt))-g)dt$
$\implies 0=\dfrac{F}{Km}(sin(Kt_0)-\mu +\mu cos(Kt_0))-gt_0$

Since $\dfrac{\pi}{2}=Kt_0\implies t_0=\dfrac{\pi}{2K}$
$\implies 0=\dfrac{F}{Km}(1-\mu )-\dfrac{g\pi}{2K}$
$\implies F=\dfrac{mg\pi}{2(1-\mu)}$

Gitanjali Rout

8 Years ago

JHVH $\implies F=\dfrac{mg\pi}{2(1-\mu)}$ $\implies 0=\dfrac{F}{Km}(1-\mu )-\dfrac{g\pi}{2K}$ $\dfrac{\pi}{2}=Kt_0\implies t_0=\dfrac{\pi}{2K}$ Since $\implies 0=\dfrac{F}{Km}(sin(Kt_0)-\mu +\mu cos(Kt_0))-gt_0$ $\implies \int_0^0 dv=\int_0^{t_0}(\dfrac{F}{m}(cos(Kt)-\mu sin(Kt))-g)dt$ $\implies v=\int_0^{\pi/2}(\dfrac{F}{m}(cos(Kt)-\mu sin(Kt))-g)dt$ $=\dfrac{F}{m}(cos(Kt)-\mu sin(Kt))-g$ $\implies \dfrac{dv}{dt}=\dfrac{Fcos\theta-mg-\mu (Fsin\theta)}{m}$ $Fcos\theta-mg-\mu (Fsin\theta)=ma$ Net force acting on the body upwards=

…............................................................................................................................................................

Forum Team

8 Years ago

Gitanjali, please stop copy pasting answers posted by other users. You will not be rewarded for these points and your account will be blocked due to this activity as it is against forum guidelines. Please check the guidelines here – Forum point Policy – https://www.askiitians.com/forum-point-policy/

Thanks

Forum Team

Three identical balls are placed on a frictionless horizontal surface touching each other. They stick to each other because of adhesive. Another ball of same radius and mass m is placed over the void created by the three balls. Find the forces applied by the balls kept on the floor to each other if the system remains in equilibrium.

mechanics

1 Answer Available

Last Activity: 10 Months ago

A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.

11
21
31
41

mechanics

1 Answer Available

Last Activity: 10 Months ago

A metal strip clamped at one end vibrates with a frequency of 20 Hz and amplitude of 5 mm
at the free end, where a small mass of 2 g is positioned. determine
(i) The velocity of the end when passing through the zero position
(ii) The acceleration at maximum displacement
(iii) The maximum kinetic energy of the mass

mechanics

2 Answers Available

Last Activity: 3 Years ago

An object of mass m = 0.25 kg oscillates in a fluid at the end of a vertical spring of spring
constant kH = 85 N/m, see Fig.1. The effect of the fluid resistance is governed by the
damping constant b = 0.07kg/s.
(i) Find the period of the damped oscillation.
(ii) By what percentage does the amplitude of the oscillation decrease in each cycle?

mechanics

1 Answer Available

Last Activity: 3 Years ago

If a=x² find the displacement at t =3sec if body velocity at t= 0 sec is 0

mechanics

1 Answer Available

Last Activity: 3 Years ago

View all Questions