Answer to Question #290654 in Optics for Mark

Question

Activity Title: Mechanical Energy

Learning Target : To determine the mechanical energy of a system. Consider a simple pendulum with a bob mass 4.2 kg

Questions:

1. If the speed of the bob at the lowest point B is 0.84 m/s , What is its kinetic energy at this point?

2. If points A and C are the highest points reached by the bob, What is the potential energy if h= 0.036m at these points.?

3. What is the kinetic energy of the bob points A and C ?

4. What is the potential energy at point B.?

5. What is the total mechanical energy at point A.?

6. What is the total mechanical energy at point B.?

Answer 1

Gives

M=4.2kg

Point B velocity

$V_B=0.84m/sec$

Point A and C hiegh

h=0.036m

Part(a)

Kinetic energy of lowest point

$K_B=\frac{1}{2}mv^2$

$$K_B=0.5\times4.2\times(0.84)^2=1.48176J$$

Part(b )

Point (A) and Point (B) potential energy

$PE=mgh$

PE=$4.2\times9.8\times0.036=1.48176J$

$PE_{A}=PE_{C}=1.48176J$

Part (c)

Kinetic energy of point ( A)and (c)

$KE_{A}=KE_{C}=0$

At Point( a) and point( c) kinetic energy equal zero

part(d)

Potential energy at point B

$PE_{B}=0J$

At Point (B) potential energy is zero

part(e) total machanical energy point (A)

(Machanical energy )$_A$ =

$$KE_A+PE_B$$

Machanical energy at point (A) =0+mgh

ME=mgh

ME=1.48176J

Part(f)

Machanical energy at point (B)

$ME=KE_B+PE_B$

$ME=\frac{1}{2}mv^2+0$

Mechanical energy at point B

$ME_B=1.48176+0=1.48176J$