An object with a mass of #15 kg# is moving at #9 m/s# over a surface with a kinetic friction coefficient of #4 #. How much power will it take to accelerate the object at #3 m/s^2?

2 Answers
Jan 13, 2018

Frictional force acting on the object is # fk#= #u* N# or, umg i.e 600 N,
So, let's assume we will be requiring a force of F to accelerate the object at 3 #(m/sec^2)#
So,using equation of force we can write,
#(F - fk)# = #ma#
Or, F = #(15*3)#+600 N i.e 645 N
Now,if this force cause displacement s of the object wi th in time t,power will be (work done/time) i.e 645#(s/t)#

Jan 13, 2018

The power is #=5.697kW#

Explanation:

The mass of the object is #m=15kg#

The speed is #u=9ms^-1#

The acceleration is #a=3ms^-2#

The coefficient of kinetic friction is

#mu_k=F_r/N=4#

The normal force is #N=15gN#

The frictional force is #F_r=mu_k xx N=4*15g=60gN#

The force necessary to accelerate the object is #=FN#

The acceleration due to gravity is #g=9.8ms^-2#

According to Newton's Second Law

#F-F_r=ma#

#F=ma+F_r=((15xx3)+(60g))N=633N#

#"Power"="Force"xx "velocity"#

The power is

#P=Fxxv=633*9=5697W#