Answer:
a) 4.98m/s²
b) 481.66N
Explanation:
a) Using the Newtons second law of motion
m is the mass of the object
g is the acceleration due to gravity
Fm is the moving force acting along the plane
Ff is the frictional force opposing the moving froce
a is the acceleration of the skier
Given
m = 60kg
g = 9.8m/s²
= 35°
Ff = 38.5N
Required
acceleration of the skier a
Substituting into the formula;
Hence the acceleration of the skier is 4.98m/s²
b) The normal force on the skier is expressed as;
N = Wcosθ
N = mgcosθ
N = 60(9.8)cos 35°
N = 588cos 35°
N = 481.66N
Hence the normal force on the skier is 481.66N
<h2>
Answer:</h2>
143μH
<h2>
Explanation:</h2>
The inductance (L) of a coil wire (e.g solenoid) is given by;
L = μ₀N²A / l --------------(i)
Where;
l = the length of the solenoid
A = cross-sectional area of the solenoid
N= number of turns of the solenoid
μ₀ = permeability of free space = 4π x 10⁻⁷ N/A²
<em>From the question;</em>
N = 183 turns
l = 2.09cm = 0.0209m
diameter, d = 9.49mm = 0.00949m
<em>But;</em>
A = π d² / 4 [Take π = 3.142 and substitute d = 0.00949m]
A = 3.142 x 0.00949² / 4
A = 7.1 x 10⁻⁵m²
<em>Substitute these values into equation (i) as follows;</em>
L = 4π x 10⁻⁷ x 183² x 7.1 x 10⁻⁵ / 0.0209 [Take π = 3.142]
L = 4(3.142) x 10⁻⁷ x 183² x 7.1 x 10⁻⁵ / 0.0209
L = 143 x 10⁻⁶ H
L = 143 μH
Therefore the inductance in microhenrys of the Tarik's solenoid is 143
a) At a position of 2.0m, the Initial energy is
all made up of the potential energy=m*g*hi<span>
and meanwhile at 1.5 all its energy is also potential energy=m*g*hf
The percentage of energy remaining is E=m*g*hi/m*g*hf x 100
and since mass and gravity are constant so it leaves us with
just E=hi/hf
which 1.5/2.0 x100= 75% so we see that we lost 25% of the
energy or 0.25 in fraction
b) Here use the equation vf^2=vi^2+2gd
<span>where g is gravity, vf is the final velocity and vi is the
initial velocity while d is the distance travelled
so in here we are looking for the vi so let us isolate that
variable
we know that at maximum height or peak, the velocity is 0 so
vf is 0
therefore,</span></span>
vi =sqrt(-2gd) <span>
vi =sqrt(-2x-9.81x1.5) </span>
<span>vi =5.4 m/s
<span>c) The energy was converted to heat due to friction with the
air and the ground.</span></span>
First question: 800J
Second question: 20.4m
