Question

A pendulum consisting of a massless string of length 20 cm and the tide bob of mass 100 gram is setup has the conical pendulum its bob not perform 75 grams calculate the kinetic energy and increase in the gravitational potential energy of the bob

Answer 1

Answer:

Explanation:given that l = 0.2 m

Mass (m) = 0.1 kg

Frequency (n) = 75/60 rps which is nearly 1.25 rps and hence period = 0.8 sec

Answer 2

The value of K.E 0.0443 J and P.E = 0.0394 J

Explanation:

We are given that:

• Length of string = 20 cm = 0.2 m
• Mass of bob = 100 g
• To find K.E and P.E

Solution:

T = 2π √ l cosθ / g

cos θ = T^2 g^2 / 4 π^2 l

Cos θ  = (0.8)^2 x (π^2) / 4 π^2 x 0.2

Cos θ = 0.8

P.E = mgl ( 1 - cos θ)

K.E = 1/2 mv^2

K.E = P.E

V^2 = 2gl ( 1 - cosθ)

V =  √ 2gl ( 1 - cosθ)

V = √  2 x 9.8 x 0.2 ( 1 - 0.8) = 0.8876 m/s

K.E = 1.2 mv^2 = 1/2  0.1 x 0.8876 = 0.0443 J

P.E =  mgl ( 1 - cos θ)

P.E = 0.1 x 9.8 x 0.2 ( 1 - 0.8)

P.E = 0.0394 J