While leaning out a window that is 6.4 m above the ground, you drop a 0.60-kg basketball to a friend at ground level. Your friend catches the ball at a height of 1.4 m above the ground. Determine the following.
(a) the amount of work done by the force of gravity on the ball
(b) the gravitational potential energy of the ball-earth system, relative to the ground when it is released
(c) the gravitational potential energy of the ball-earth system, relative to the ground when it is caught
(d) the ratio of the change (PEf − PE0) in the gravitational potential energy of the ball-earth system to the work done on the ball by the force of gravity

Explanation:

Given that,

Height of window (h)=6.4m

Mass of basketball M=0.6kg

If the ball is cough at a height of 1.4m

Let g=9.81m/s²

a. Work done by gravity is given by

weight =mg

Work done by the weight of the body is weight of the body times height of the body from the ground

Wg=w•h

Wg=mgh

The work is done to where the ball was caught is height i.e h=6.4-1.4

h=5m

Wg=0.6×9.81×5

Wg=29.43J

b. Gravitation potential energy relative to the ground is give as

Wp=mgh

This is the potential energy over the whole height i.e h=6.4m

Wp=0.6×9.81×6.4

Wp=37.67J

c. Gravitational potential energy relative to when the ball was caught

The height when the ball was caught is 1.4m

Therefore, potential energy is given as

Wp=mgh

Wp=0.6×9.81×1.4

Wp=8.24J

d. Ratio of change in potential energy to the work done

∆P.E= P.E(final)-P.E(initial)

∆P.E= 8.24-37.67

∆P.E= -29.43

The ratio will be ∆P.E/Wg

Ratio= -29.43/29.43

Ratio= -1

Which is right

Because work is conservative and

W=-∆U

Then

W/∆U=-1

gets less

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: