A block of mass 45.0 kg is sliding on top of a frictionless horizontal surface w

Question

A block of mass 45.0 kg is sliding on top of a frictionless horizontal surface with a momentum of magnitude 87.0 kgm/s that is pointing northward. Starting at some time say 0 s , a force of magnitude F=(8.20 N/s )t is applied to the block and is directed southward. This is the only horizontal force on the block.

Part A:

When, i.e. at what value of t, will this block have a momentum of magnitude 56.5 kgm/s directed southward?

Part B:

Calculate the net work done on the block by the force in the time interval from t=0 sto the time calculated in part A?

Part C:

With what magnitude is the block accelerating at the time calculated in part A?

Explanation / Answer

Here ,

initial momentum , Pi = 87 Kg.m/s

force , F = -8.2 N

part A)

let the time is t

Pf = Pi + Force * t

-56.5 = 87 - 8.2 * t

t = 17.5 s

the time t is 17.5 s

b)

net work done = change in kinetic energy

net work done = (pf^2 - pi^2)/2m

net work done = (56.5^2 - 87^2)/(2 * 45)

net work done = -48.43 J

c)

let the acceleration is a

Using second law of motion

a = F/m

a = 8.2/45

a = 0.182 m/s^2

the magnitude of acceleration is 0.182 m/s^2

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