Question

A particle of mass 2 kg moving
along x axis is being acted upon by
a single conservative force denoted
by" (*). The potential energy of the
i U (x) = 20+(x-2)',
particle is
where U is in joule and is in metre.
The velocity that the particle
possesses at x = 5m is 4 ms -1
Based on the above facts, answer
the following questions.
The system possesses a
mechanical energy equal to​

Answer 1

Answer:

39 Joules

Explanation:

The mechanical energy of the system would be a sum of the potential energy and kinetic energy.

The potential energy of the system is U (x) = 20+(x-2)

Now to find the energy at x =5

P.E  = 20 + (5-2)

P.E = 23

Now at this point, velocity is 4ms-1

Kinetic energy would be;

K.E = 1/2 mv^2

K.E = 1/2 (2) x (4)^2

K.E = 16

Total mechanical energy = 23 + 16 = 39 Joules

Answer 2

Total mechanical energy possessed by the system is 39 joules.

Explanation:

Given data:

• Mass of particle = 2 Kg
• Potential energy of the system = U (x) = 20 + (x - 2)
• To Find: The mechanical energy of the system = ?

Solution:

Mechanical energy = Kinetic energy + Potential energy

Find the energy at point x =5

Put the value of x in the above equation.

P.E = 20 + (5 - 2)

P.E = 23

We are given that the velocity is 4ms-1  at x = 5 m.

Now find the kinetic energy.

K.E = 1/2 mv^2

K.E = 1/2 (2) x (4)^2

K.E = 16

Total mechanical energy = K.E + P.E = 23 + 16 = 39 Joules