Question

A particle of mass 2.5 kg moves in a conservative force field. Its potential energy curve
is shown below. From the curve, determine (a) the total mechanical energy of the
particle at x = 1.3 m if it has a speed of 8 ms−1 and (b) the minimum total energy at
which the particle can escape from the force field. If Etot = 150 J, where would the
particle have (i) zero velocity, (ii) maximum velocity

Answer 1

Answer on Question #61697-Physics-Mechanics | Relativity

A particle of mass $2.5\mathrm{kg}$ moves in a conservative force field. Its potential energy curve is shown below. From the curve, determine (a) the total mechanical energy of the particle at $x = 1.3\mathrm{m}$ if it has a speed of 8 ms-1 and (b) the minimum total energy at which the particle can escape from the force field. If Etot = 150 J, where would the particle have (i) zero velocity, (ii) maximum velocity

Solution

(a)

$$E _ {t o t} (1. 3) = E (1. 3) + \frac {m v ^ {2}}{2} = 1 5 0 + \frac {1}{2} 2. 5 (8) ^ {2} = 2 3 0 J.$$

(b) The minimum total energy at which the particle can escape from the force field is

$$E _ {t o t} = E (\infty) + \frac {m 0 ^ {2}}{2} = 2 5 0 J.$$

(i)

$$E = 1 5 0 J \rightarrow x = 1. 3 m o r 3. 4 m.$$

(ii) Maximal velocity would be at the minimum of potential energy.

$$X = 2. 6 m.$$