Asmall box is held in place against a rough vertical wall bysomeone pushing on it with a force directed upward at 28 degreesabove horizontal. the coeffients of static and kineticfriction between the box and the wall are 0.40 and 0.30,respectively. the box slides down unless the applied forcehas a magnitude 23n. what is the mass of the box?

m = 1.9287 Kg

Explanation:

Given

∅ = 28º

μs = 0.40

μk = 0.30

F = 23 N

m = ?

We can apply  

∑Fh = 0  (+→)

N - Fh = 0    ⇒  N = Fh = F*Cos ∅

then    N = F*Cos ∅

∑Fv = 0  (+↑)

⇒    Fy - W + Ff = 0

where

Fy = F*Sin ∅

W = m*g

Ff = μs*N = μs*F*Cos ∅

then

⇒    Fy - W + Ff = F*Sin ∅ - m*g + μs*F*Cos ∅ = 0

⇒    m = (F / g)*(Sin ∅ + μs*Cos ∅)

⇒    m = (23 N / 9.81 m/s²)*(Sin 28º + 0.40*Cos 28º)

⇒    m = 1.9287 Kg

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: