– A 5.00-kg body accelerates from 3.25 m/s to 9.75 m/s in 3.0 seconds when a force acts upon it. Find (a) the change in momentum

Question

A 5.00-kg body accelerates from 3.25 m/s to 9.75 m/s in 3.0 seconds when a force acts upon it. Find (a) the change in momentum of the body, (b) the impulse produced by the force, and (c) the magnitude of the force.​

in progress 0
Khánh Gia 2 months 2021-07-26T00:17:44+00:00 2 Answers 3 views 0

Answers ( )

    0
    2021-07-26T00:19:20+00:00

    Answer:

    (a) the change in momentum of the body is 32.5 kg.m/s

    (b) the impulse produced by the force is 32.5 N.s

    (c) the magnitude of the force is 10.83 N

    Explanation:

    Given;

    mass of the body, m =  5.00-kg

    initial velocity of the body, u = 3.25 m/s

    final velocity of the body, v = 9.75 m/s

    time taken, t = 3.0 seconds

    Part (a) the change in momentum of the body

    ΔP = mv – mu

         = (5 x 9.75) – (5 x 3.25)

         = 48.75 – 16.25

         = 32.5 kg.m/s

    Part (b) the impulse produced by the force

    I = f x t

    where;

    I is impulse

    f is the applied force

    t is time

    f x t = mΔv

    I = mΔv

    I = m (v -u)

    I = 5 (9.75 – 3.25)

    I = 32.5 N.s

    Part (c) the magnitude of the force;

    I = f x t​

    f = I / t

    where;

    f is magnitude of the force.

    I is impulse

    t is time

    f = 32.5 / 3

    f = 10.83 N

    0
    2021-07-26T00:19:41+00:00

    Answer:

    (a) 32.5 kgm/s

    (b) 32.5 Ns

    (c) 10.8 N

    Explanation:

    The change in momentum can be calculated from the definition of linear momentum:

    \Delta p=\Delta (mv)= m \Delta v\\\\\Delta p= (5.00kg)(9.75m/s-3.25m/s)\\\\\Delta p=32.5kgm/s

    Then, the change in momentum of the body is of 32.5 kgm/s (a).

    Now, from the impulse-momentum theorem, we know that the change in momentum of a body \Delta p is equal to the impulse I exerted to it. So, the impulse produced by the force equals 32.5 kgm/s (or 32.5 Ns) (b).

    Finally, since we know the value of the impulse and the interval of time, we can easily solve for the magnitude of the force:

    I=F\Delta t\\\\\implies F=\frac{I}{\Delta t}\\\\F=\frac{32.5Ns}{3.0s}\\\\F=10.8N

    It means that the magnitude of the force is of 10.8N (c).

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )