A pendulum has a length of 70cm and a bob of mass 1.1kg. Please help !?

M

Manny Paps

New member
when the string is at 25 degrees to the interval, the bob has a speed of 3m/s

what is the maximum speed of the bob? and what is the max angle to the vertical?
 
Use trig with the angle and length to get the height of the bob above the lowest point. Then you can get the total energy, potential plus kinetic:
Kinetic Energy in J if m is in kg and V is in m/s
KE = ½mV²
Potential Energy in J
PE = mgh

so the energy at that point is ½mV² + mgh

max speed is at the lowest point, when PE is zero and all of the energy is KE, so you can get the speed by setting KE equal to the above total, KE = ½mV² and solve for V.

Max height you get from PE, since KE is zero as speed is zero. so take the energy from the first part and set it equal to mgh and solve for h.

Now use trig to get the angle from the height.

.
 
By the Law of energy conservation:-
=>E(total) = KE + PE
=>E = 1/2mv^2 + mgh
=>E = 1/2mv^2 + mg(L-Lcos?)
=>E = 1/2 x 1.1 x (3)^2 + 1.1 x 9.8 x (0.7 - 0.7 x cos25*)
=>E = 5.66 J
=>By E = KE(max)
=>5.66 = 1/2mv^2
=>5.66 = 1/2 x 1.1 x v^2
=>v = ?10.29
=>v = 3.21 m/s
By E = PE(max)
=>5.66 = mgh
=>5.66 = 1.1 x 9.8 x [0.7 - 0.7 x cos?]
=>cos? = 0.25 = cos75*
=>? = 75*
 
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