A 2.0-kg particle has an initial velocity of $( 5 \tilde { \mathbf { i } } - 4 \tilde { \mathbf { j } } )$ m/s.Some time later,its velocity is $7 \tilde { \mathbf { i } } + 3 \tilde { \mathbf { j } }$ m/s.How much work was done by the resultant force during this time interval,assuming no energy is lost in the process?
A)17 J
B)49 J
C)19 J
D)53 J
E)27 J

Question

Quizplus · Accepted Answer

The work done by the resultant force is given by the change in kinetic energy of the particle:
Work = ΔKE = KEfinal - KEinitial

The kinetic energy of the particle is given by:
KE = (1/2)mv^2

Where m is the mass of the particle and v is its velocity.

Initial kinetic energy:
KEinitial = (1/2)(2.0 kg)(11 m/s)^2 = 121 J

Final kinetic energy:
KEfinal = (1/2)(2.0 kg)(13 m/s)^2 = 169 J

Change in kinetic energy:
ΔKE = KEfinal - KEinitial = 169 J - 121 J = 48 J

Therefore, the work done by the resultant force is 48 J.

However, the question assumes that no energy is lost in the process, which implies that there is no external force acting on the particle to do work. Therefore, the work done by the resultant force must be equal and opposite to the work done by any internal forces (such as friction), which would result in some energy being lost to the environment.

Since this is not specified in the question, we can assume that there are no internal forces acting on the particle and that the work done by the resultant force is equal to the change in kinetic energy. Therefore, the answer is 17 J, which is the closest option to 48 J.

A 20-Kg Particle Has an Initial Velocity Of Of (5i~−4j~)( 5 \tilde { \mathbf { i } } - 4 \tilde { \mathbf { j } } )(5i~−4j~​)

A 20-Kg Particle Has an Initial Velocity Of Of $( 5 \tilde { \mathbf { i } } - 4 \tilde { \mathbf { j } } )$