Why do we see the color black?
1 answer:
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Answer:
b. mg ( μ · cos θ + sin θ)
Explanation:
Hi there!
Please, see the attached figure for a graphical description of the problem.
We have the following parallel forces acting on the block (in parallel direction to the direction of movement):
F = applied force.
Fr = friction force.
wx = parallel component of the weight.
According to Newton´s second law:
∑F = m · a
Where "m" is the mass of the block and "a" its acceleration.
Then:
F - Fr - wx = m · a
Since the block is to be pushed at a constant velocity, the acceleration is zero. Then:
F - Fr - wx = 0
F = Fr + wx
The applied force has to be equal to the friction force plus the parallel component of the weight to push the block at constant velocity.
The friction force is calculated as follows:
Fr = μ · N
Where N is the normal force and μ is the coefficient of friction.
Notice that the normal force is of the same magnitude as the perpendicular component of the weight, wy.
Let´s apply Newton´s second law in the perpendicular direction to show this:
∑F = m · a
N - wy = m · a
The acceleration of the block in the perpendicular direction is zero. Then:
N - wy = 0
N = wy
And wy can be obtained by trigonometry (see figure):
wy = W · cos θ
N = wy = mg · cos θ
The parallel component of the weight is calculated using trigonometry (see figure):
wx = W · sin θ
wx = mg · sin θ
Then the applied force will be:
F = Fr + wx
F = μ · N + mg · sin θ (N = wy = mg · cos θ)
F = μ · mg · cos θ + mg · sin θ
F = mg ( μ · cos θ + sin θ)
The correct answer is the b.
Answer:
The total distance will be 400 m.
Explanation:
For portion AB:
Acceleration = 2
t= 10 s
Car start from rest , u=0 m/s
We know that
S= 100 m.
For portion BC:
V= u + at
V=0 + 2 x 10
V= 20 m/s
In this portion car moves with constant velocity 20 m/s for 10 s.
So distance S= V x t
S=20 x 10 =200 m.
For portion CD:
The velocity at point C will be 20 m/s
In this portion the final speed of car will be zero because given that at final car come to rest.
So the acceleration will be in the negative direction to stop the car.
We know that
S=100 m
The total distance AD=AB + BC+ CD
AD=100 +200 + 100 m
AD=400 m.
The total distance will be 400 m.
