Question

A 3.2 kg ball that is moving straight upward has 17 Joules of kinetic energy. The total mechanical energy is 25 Joules.

Answer 1

Answer:

h = 0.25 [m]

v = 3.26 [m/s]

Explanation:

In order to solve this problem, we must remember that mechanical energy is defined as the sum of kinetic energy plus potential energy.

E1 = Ek + Ep

where:

E1 = mechanical energy = 25 [J]

Ek = kinetic energy = 17 [J]

Ep = potential energy [J]

25 = 17 + Ep

Ep = 8 [J]

Now the potential energy is defined by the following equation:

Ep = m*g*h

where:

m = mass = 3.2 [kg]

g = gravity acceleration = 9.81 [m/s²]

h = elevation [m]

8 = 3.2*9.81*h

h = 0.25 [m]

The velocity can be calculated by means of kinetic energy.

$E_{k} =\frac{1}{2} *m*v^{2}\\17 =\frac{1}{2} *3.2*v^{2} \\v= \sqrt{\frac{17*2}{3.2} }\\v = 3.26[m/s]$