11. The potential energy of a system of two particles separated by a distance r

Question

11. The potential energy of a system of two particles separated by a distance r is given by U(r) =A/r, where A is a constant. Find the radial force F. that each particle exerts on the other. 12. A baseball outfielder throws a 0.150-kg base- ball at a speed of 40.0 m/s and an initial angle of 30.0 degree to the horizontal. What is the kinetic energy of the baseball at the highest point of its trajectory? 13. An 820-N Marine in basic training climbs a 12.0-m W vertical rope at a constant speed in 8.00 s. What is his power output?

Explanation / Answer

as we know,
if force is denoted as F(r) and energy is denoted as U(r),
then F=-dU/dr

here given that,
U(r)=A/r

then dU/dr=-A/r^2

then F(r)=-dU/dr=A/r^2

hence the force as a function of distance r is given as
F(r)=A/r^2.

Q2. mass of the base ball=m=0.15 kg
initial speed=u=40 m/s

initial angle=30 degrees

at highest point of the trajectory, the vertical component of the veloicty will be zero.

the horizontal component=horizontal component of initial velocity(as there is no horizontal acceleration)

=40*cos(30)=

so kinetic energy at the highest point=0.5*0.15*34.641^2=90 J

Q3.

as we know, power=force*speed

speed=displacement/time

here force=820 N
displacement=12 m
time=8 seconds

hence power=820*12/8=1230 W

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