Answer:
Part a)
Part b)
T = 4.68 s
Explanation:
Part a)
Shell is fired at speed of 40 m/s at angle of 35 degree
so here we have
since gravity act opposite to vertical speed of the shell so at the highest point of its trajectory the vertical component of the speed will become zero
so at the highest point the speed is given
Part b)
After completing the motion we know that the displacement of the object will be zero in Y direction
so we have
The compression of 10 cm by a 100 N force on the plane that has a
coefficient of friction of 0.39 give the following values.
Mass of the block, m = 3 kg
Coefficient of kinetic friction, = 0.39
Therefore, we have;
Friction force = ·m·g·cos(θ)
Which gives;
Friction force = 0.39 × 3 × 9.81 × cos(48°) ≈ 7.68
Work done by the motion of the block, <em>W</em> ≈ 7.68 × d
The work done = The kinetic energy of the block, which gives;
The initial kinetic energy in the spring is found as follows;
K.E. = 0.5 × 1000 N/m × (0.1 m)² = 5 J
The initial velocity of the block is therefore;
5 = 0.5·m·v²
v₁ = √(2 × 5 ÷ 3) ≈ 1.83
Work done by the motion of the block, <em>W</em> ≈ 7.68 N × 0.07 m ≈ 0.5376 J
Chane in kinetic energy, ΔK.E. = Work done
ΔK.E. = 0.5 × 3 × (v₁² - v₂²)
Which gives;
ΔK.E. = 0.5 × 3 × (1.83² - v₂²) = 0.5376
Which gives;
The height at which the block will stop moving, <em>h</em>, is given as follows;
Which gives;
The distance up the inclined, the block rises, at maximum height is therefore;
≈ 1.536 m
Therefore;
h = 1.536 × sin(48°) ≈ 1.1415
From the above solution for the height, the length of the incline is he
distance along the incline at maximum height which is therefore;
Learn more about conservation of energy here:
1) The gravitational force between Ellen and the moon is
2) The two forces are equal, while the acceleration of the bus is smaller than the acceleration of the bicycle.
Explanation:
1)
The magnitude of the gravitational force between two objects is given by
where
is the gravitational constant
are the masses of the two objects
r is the separation between them
In this problem, we have:
is the mass of Ellen
is the mass of the moon
is the distance between Ellen and the moon
Substituting, we find the gravitational force between Ellen and the moon:
2)
We can analyze the forces acting in the collision between the bus and the bicycle by using Newton's third law of motion, which states that:
"When an object A exerts a force (called action) on an object B, then object B exerts an equal and opposite force (called reaction) on object A"
Applied to our problem, this means that the force exerted by the bus on the bicycle during the collision (action force) is equal (and opposite) to the force exerted by the bicycle on the bus (reaction force).
Now let's analyze the accelerations of the two vehicles. We can find the acceleration of each vehicle by using Newton's second law:
where
a is the acceleration
F is the force exerted on the vehicle
m is the mass of the vehicle
As we said previously, the force F exerted on each of the two vehicles: so, the acceleration only depends on the mass. In particular, the acceleration is inversely proportional to the mass: therefore, the larger the mass of the vehicle, the smaller the acceleration. This means that the acceleration of the bus is smaller than the acceleration of the bicycle.
Learn more about gravitational force:
And about Newton's third law:
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