A certain constant force F 0 is applied to an object for a given time T: the obj

Question

A certain constant force F0 is applied to an object for a given time T: the object starts from rest. A force F0/2 is then applied to an identical abject, also starting from rest, for a time 2T. Compare (a) the distance traveled during the time of application of the froces,(b) velocities at the end of the time periods, and (c) accelerations at the end of the time periods in the two cases. For each quantity, state whether you expect the two values to be equal or unequal; if unequal which should be greater?

Explanation / Answer

( a ) a1 = F0 / m ;

a2 = F0 / 2m   ;

since x = 0.5 a t ^2 ;

x1 = 0.5 ( F0 / m ) T^2 ;

x2 = 0.5 ( F0 / 2m ) ( 2T) ^2 = 2x1 ;

so distance travelled in 2nd object is more than first ;    x2 > x1 ;

( b ) v = at ;

v1 = ( F0 / m ) ( T ) ;

v2 = ( F0 /2m ) ( 2T) = v1 ;

so the velocities in both the cases is the same ; v1 = v2 ; ( velocities at the end )

( c )  

a1 = F0 / m ;

a2 = F0 / 2m = 1 / 2 a1 ;

so acceleration in second case is half in the first case , or a2 < a1 ;

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.