A1.1 g marble is fired vertically upward using a spring gun. the spring must be compressed 6.2 cm if the marble is to just reach a target 16 m above the marble's position on the compressed spring. (a) what is the change δug in the gravitational potential energy of the marble-earth system during the 16 m ascent

ΔU = 0.17 J

Explanation:

m = 1.1 g = 1.1*10⁻³ Kg

h₁ = 6.2 cm = 0.062 m

h₂ = 16.062 m

ΔU = ?

We apply the formulas

U₁ = m*g*h₁

U₂ = m*g*h₂

ΔU = U₂ - U₁ = m*g*h₂ - m*g*h₁ = m*h*(h₂ - h₁)

⇒  ΔU = (1.1*10⁻³ Kg)*(9.81 m/s²)*(16.062 m - 0.062m)

⇒  ΔU =  0.17 J

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.