Achild playing in a swimming pool realizes that it is easy to push a small inflated ball under the surface of the water whereas a large ball requires a lot of force. the child happens to have a styrofoam ball (the shape of the ball will not distort when it is forced under the surface), which he forces under the surface of the water. if the child needs to supply 608 n to totally submerge the ball, calculate the diameter of the ball. the density of water is =1.000×103 kg/m3, the density of styrofoam is =95.0 kg/m3, and the acceleration due to gravity is =9.81 m/s2.

Explanation:

Here the buoyancy is in equilibrium with the weight of the ball and the force the child applies: B=W+F=mg+F

The mass of the ball will be given by its volume and density:

And the buoyancy is the weight of the fluid displaced (water for us), in our case, this volume of fluid displaced is equal to the volume of the ball:

Putting all together:

Using the formula for the volume of a sphere we have then:

Or in terms of the diameter:

Which for our values is:

the average speed is 24.57 km/hr

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: