A61 kg skier on level snow coasts 184 m to a stop from a speed of 12 m/s. (a) use the work-energy theorem to find the coefficient of kinetic friction between the skis and snow. (b) suppose a 75 kg skier with twice the starting speed coasted the same distance before stopping. find the coefficient of kinetic friction between that skier’s skis and the snow.

a) μ = 0.0398

b) μ = 0.1595

Explanation:

a) d = 184 m

Vi = 12 m/s

vf = 0 m/s

m = 61 Kg

μ = ?

We use the equation

W = Kf - Ki  (I)

then we have

W = F(friction)*d = - μ*N*d = - μ*m*g*d  (II)

Kf = m*(vf)²/2 = m*(0)²/2 = 0 J

If (I) = (II)

0 - m*(vi)²/2 = - μ*m*g*d    ⇒   μ = (vi)² / (2*g*d)

⇒   μ = (12 m/s)² / (2*9.81 m/s²*184 m) = 0.0398

b) d = 184 m

Vi = 24 m/s

vf = 0 m/s

m = 75 Kg

μ = ?

We use the equation

W = Kf - Ki  (I)

then we have

W = F(friction)*d = - μ*N*d = - μ*m*g*d  (II)

Kf = m*(vf)²/2 = m*(0)²/2 = 0 J

If (I) = (II)

0 - m*(vi)²/2 = - μ*m*g*d    ⇒   μ = (vi)² / (2*g*d)

⇒   μ = (24 m/s)² / (2*9.81 m/s²*184 m) = 0.1595

The mass of the skier is not important in the analysis.

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: