Answer:
a) θ = 12.12°
b) equal to 0.21g
Explanation:
Solution:-
Declare variables:
- The mass of solid sphere, m
- The inclination angle, θ
- The linear acceleration a down the slope of the solid sphere is a = 0.21g
Where, g: The gravitational acceleration constant.
- The component of weight of solid sphere directed down the slope is given by:
Ws = m*g*sin ( θ )
- Apply Newton's second law of motion down the slope, state:
F_net = m*a
- The only net force acting on the solid sphere is the Weight. So, the equation of motion in the coordinate axis ( down the slope ).
Ws = m*a
m*g*sin ( θ ) = m*0.21*g
- Solve for inclination angle ( θ ):
sin ( θ ) = 0.21
θ = arcsin ( 0.21 )
θ = 12.12°
- If a friction-less block of mass ( m ) moves down the same slope then block has weight component down the slope as:
Wb = m*g*sin ( θ )
- Apply Newton's second law of motion down the slope, state:
F_net = m*a
- The only net force acting on the solid sphere is the Weight. So, the equation of motion in the coordinate axis ( down the slope ).
Ws = m*a
m*g*sin ( θ ) = m*a
- Solve for linear acceleration ( a ):
g*sin ( θ ) = a
a = sin ( 12.12 ) * g
a = 0.21g
Answer: The acceleration is independent of mass and only depends on the inclination angle θ.
