A sphere rolls down an inclined plane at 30°. Calculate its acceleration.
Abhijeet , 6 Years ago
Grade 11
Mechanics> A sphere rolls down an inclined plane at ...
1 Answers
Dinesh Nayak
Last Activity: 6 Years ago
On rolling down the slope the potential energy of the sphere decreases and kinetic energy increases also the total kinetic energy is equal to the sum of both rolling and translation kinetic energies.
So,
Loss of kinetic energy = gain of kinetic energy
Mgh = ½ MV2 + ½ I * (omega)2 [angular velocity]
now we know, from the radius of gyration: I = M * K2
v = r (radius) * omega
Mgh = ½ MV2 + ½ (M*K2) * (v/r)2
2gh = v2 [ 1 + (K/r)2 ]
Now we are familiar with the equation
v2 – u2 = 2as, where u (initial velocity) =0
so, we get a = v2 / 2s
where ‘s’ is the total path (hypotanuse) which is at a height ‘h’
so Sin (theta) = h / s
Sin (30 degrees) = h/s
½ = h/s
So s = 2h
so from this we get : a = v2 / 2(2h) = v2 / 4h
now substituting the value for v2
2gh = a(4h) [ 1+ (K/r)2 ]
a = [2gh / 4h] [ 1 + (K/r)2 ]
so the equation for acceleration at 30° :
a = [g / 2] [ 1 + (K/r)2 ]
a = [g / 2] [ 1 + (K/r)2 ]
Provide a better Answer & Earn Cool Goodies
Enter text here...
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
Other Related Questions on Mechanics
A metal strip clamped at one end vibrates with a frequency of 20 Hz and amplitude of 5 mmat 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 Answer Available
Last Activity: 2 Year ago(s)
An object of mass m = 0.25 kg oscillates in a fluid at the end of a vertical spring of springconstant kH = 85 N/m, see Fig.1. The effect of the fluid resistance is governed by thedamping 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: 2 Year ago(s)
If a=x² find the displacement at t =3sec if body velocity at t= 0 sec is 0
Mechanics
1 Answer Available
Last Activity: 2 Year ago(s)
A particle is traveling in a circle of radius R =2.5m and with an angular velocity of 10 rad/s. What is the centripetal acceleration of the particle? The particle begins to slow down with an angular acceleration of -1 rad/s2. After 5 seconds, what is the centripetal acceleration and the tangential acceleration fo the particle?
Mechanics
1 Answer Available
Last Activity: 2 Year ago(s)
If the acceleration of block A is 5 m/s^2Find the acceleration of block B
Mechanics
1 Answer Available
Last Activity: 2 Year ago(s)