Answer:
a. WD = 65100 J
b. v = 31.4 m/s
c. 129 m
Explanation:
WD = work done (Nm or J)
F = force (N) = 310
d = distance (m) = 210
P = power (W or J/s)
m = mass (kg) = 132
a = acceleration (m/s²)
v = final velocity (m/s)
u = initial velocity (m/s)
s = displacement (m) = 210
[tex]d_{i}[/tex] = distance up incline (m)
Θ = angle of incline (°) = 23
g = gravity (m/s²) = 9.81
O = opposite
H = hypotenuse
Formulas:
WD = F.d
F (or net F) = ma
v² = u² + 2as
sin(Θ) = O/H
a.
WD = F.d
WD = 310 × 210
WD = 65100 J
b.
Ignoring friction and air resistance:
net F = 310
F = ma:
310 = 132a
a = 2.34848485
v² = u² + 2as:
v² = (0)² + 2(2.348...)(210)
v² = 986.363637
v = 31.4064267 → 31.4 m/s
c.
Coasting means no cycling by cyclist so no F produced up the incline
On incline:
F parallel to incline due to gravity = -132g.sin(23)
F parallel to incline due to gravity = -132(9.81)(0.390731128)
F parallel to incline due to gravity = -505.965552
F = ma:
net F parallel to incline = -505.965552
[tex]-505.965552 = 132a_{i}[/tex]
[tex]a_{i} = -3.83307236[/tex]
[tex](v_{i}) ^{2} = (u_{i})^{2} + 2(a_{i})(d_{i}):[/tex]
[tex]u_{i} = 31.4064267[/tex]
[tex]v_{i} = 0[/tex]
[tex](0)^{2} = (31.4064267)^{2} + 2(-3.83307236)(d_{i}) \\\\ 0 = 986.363638 - 7.66614472(d_{i}) \\\\ 7.66614472(d_{i}) = 986.363638 \\\\ d_{i} = \frac{986.363638}{7.66614472} \\\\ d_{i} = 128.664886[/tex] → 129 m
