Further Mechanics Flashcards
For a particle moving in a circle with uniform speed, what about it is not true?
The velocity of the particle is constant
For a particle moving in a circle with uniform speed, what is true about it?
The kinetic energy of the particle is constant
State the equation linking centripetal force, mass, velocity and radius.
Fcent = (mv^2) / r
Calculate the angular speed of a point on the Earth’s equator.
w = theta / time = 2 pi / (24 x 60 x 60)
A particle travels at a constant speed around a circle of radius r with centripetal acceleration a. What is the time taken for 10 complete rotations?
20 pi √r / a
A particle of mass m moves in a circle of radius r at a uniform speed with frequency f. What is the kinetic energy of the particle?
2 pi^2 m f^2 r^2
How would you find the kinetic energy of a particle that has mass m, moving in a circle of radius r with constant speed and frequency f?
Take equations w = 2 pi f; v = wr; Ek = 0.5 m v^2
v= 2 pi f r –> v^2 = 4 pi^2 f^2 r^2 –> Ek = m (2 pi^2f^2r^2)
What is the equation for calculating the angular speed of an object?
w = theta / time
State the equation for calculating the radius of an object’s orbit.
r^3 = (G x M) / w^2
In which direction does centripetal force act?
Towards the centre of the circle
A van drives over a bridge with a package inside. State the forces acting on the package.
Weight downwards, normal reaction from van upwards
Give an equation that relates the contact force, R, between the parcel and the floor of the van to m, v, r and g.
Resultant = (m v^2) / r = mg - R
Using the equation R = mg- (mv^2) / r, calculate R is m=12kg, r=23m, and v=11m/s.
R = m (g - (v^2/r)) = 12 (9.81 - (11^2 / 23)) = 54.5N
If a van driving over a bridge at a higher speed, what would happen to the reaction force R experienced by a package inside the van?
The reaction force R would decrease as the velocity of the van increases. If the van passed a certain velocity (eg 15ms), the package would loose contact with the ground as mg is constant while mv^2/r increases
What must you remember to consider when calculating tension in a string that moves in a vertical circle?
The weight force of the object
