Acrate of mass 10.6 kg is pulled up a rough incline with an initial speed of 1.51 m/s. the pulling force is 93.0 n parallel to the incline, which makes an angle of 20.1° with the horizontal. the coefficient of kinetic friction is 0.400, and the crate is pulled 5.08 m.
a) how much work is done by the gravitational force on the crate?
b) determine the increase in internal energy of the crate-incline system due friction.
c) how much work is done by the 93.0 n force on the crate?
d) what is the change in kinetic energy of the crate? e) what is the speed of the crate after being pulled 5.08 m?

a) , b) , c) , d) , e)

Explanation:

a) The work done by the gravitational force on the crate is:

b) The increase in internal energy due to friction is:

c) The work done by the external force is:

d) The change in kinetic energy is obtained from the Principle of Energy Conservation and the Work-Energy Theorem:

e) The final speed of the crate is:

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: