The only force acting on a 3.1 kg canister that is moving in an xy plane has a magnitude of 2.6 N. The canister initially has a velocity of

Question

The only force acting on a 3.1 kg canister that is moving in an xy plane has a magnitude of 2.6 N. The canister initially has a velocity of 2.3 m/s in the positive x direction, and some time later has a velocity of 6.4 m/s in the positive y direction. How much work is done on the canister by the 2.6 N force during this time?

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Thu Hương 7 months 2021-07-18T11:45:27+00:00 1 Answers 6 views 0

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    2021-07-18T11:46:58+00:00

    Answer:

    55.29 J

    Explanation:

    mass of canister, m = 3.1 kg

    magnitude of force, F = 2.6 N

    initial velocity, u = 2.3 m/s

    final velocity, v = 6.4 m/s

    Let W is the work done.

    According to the work energy theorem, the work done by all forces is equal to he change in kinetic energy.

    here F is the only force acting on the canister.

    initial kinetic energy, k = 0.5 x m x u²

    k = 0.5 x 3.1 x 2.3 x 2.3 = 8.1995 J

    final kinetic energy, k’ = 0.5 x m x v²

    k’ = 0.5 x 3.1 x 6.4 x 6.4 = 63.488 J

    So, the change in  kinetic energy,

    Δk = k’ – k

    Δk = 63.488 – 8.1995 = 55.29 J

    Thus, the work done by the force is 55.29 J.

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