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Relation between Work Done and PE

A particle, s...

Question

A particle, starting at the origin, experiences a variable force defined by F(x) = 3x 2 , causing it to move along the x-axis. How much work is done on the particle from its starting point to x = 5 ?

A

100 J

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B

125 J

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C

150 J

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D

135 J

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Solution

The correct option is B 125 J
We use our equation for the position-dependent forces:
W= $\int_{x_{0}}^{x_{f}} F (x) d x = \int_{0}^{5} 3 x 2 d x$ =[x3]05 = 53 = 125 J
The force does 125 Joules of work.

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Q. A particle, starting at the origin, experiences a variable force defined by F(x) = 3x 2 , causing it to move along the x-axis. How much work is done on the particle from its starting point to x = 5 ?

\to F = (3^i + 4^j) N

acts on a particle moving in

x - y

plane . Starting from origin, the particle first goes along

x

- axis to the point

(4 m, 0)

and then parallel to the

y

- axis to the point

(4 m, 3 m)

. The total work done by the force on the particle is

\to F = (3^i + 4^j) N

acts on a particle moving in

x - y

plane. Starting from the origin, the particle first goes along

x

- axis to the point

(4 m, 0)

and then parallel to the

y

- axis to the point

(4 m, 3 m)

. The total work done by the force on the particle is

F = - K (y ˆ i + x ˆ j)

K

is a +ve constant) acts on a particle moving in xy plane starting from origin, the particle is taken along the positive x-axis to the point (

a, 0

) and then parallel to y axis to the point (

a, a

). The total work done by force

F

on the particle is

\to F = - K (y^i + x^j)

K

is a positive constant, acts on a particle moving in the X-Y plane. Starting from the origin, the particle is taken along the positive X-axis to a point

(a, 0)

and then parallel to the y-axis to the point

(a, a)

. Calculate the total work done by the force on the particle.

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