The hoop is attached.
Consider that the friction force is given by:
F = μ·N
= μ·m·g·cosθ
We also know, considering the forces of the whole system, that:
F = -m·a + m·g·sinθ
and
a = (1/2)·<span>g·sinθ
Therefore:
</span>-(1/2)·m·g·sinθ + m·g·sinθ = <span>μ·m·g·cosθ
</span>(1/2)·m·g·sinθ = <span>μ·m·g·cosθ
</span>μ = (1/2)·m·g·sinθ / <span>m·g·cosθ
= </span>(1/2)·tanθ
Now, solve for θ:
θ = tan⁻¹(2·μ)
= tan⁻¹(2·0.9)
= 61°
Therefore, the maximum angle <span>you could ride down without worrying about skidding is
61°.</span>
Answer:
12 N/cm²
Explanation:
From the question given above, the following data were obtained:
Weight (W) of block = 240 N
Area (A) = 20 cm²
Pressure (P) =?
Next, we shall determine the force exerted by the block. This can be obtained as follow:
Weight (W) of block = 240 N
Force (F) =.?
Weight and force has the same unit of measurement. Thus, we force applied is equivalent to the weight of the block. Thus,
Force (F) = Weight (W) of block = 240 N
Force (F) = 240 N
Finally, we shall determine the pressure on the floor as follow:
Force (F) = 240 N
Area (A) = 20 cm²
Pressure (P) =?
P = F/A
P = 240 / 20
P = 12 N/cm²
Therefore, the pressure on the floor is 12 N/cm².
k = spring constant of the spring = 85 N/m
m = mass of the box sliding towards the spring = 3.5 kg
v = speed of box just before colliding with the spring = ?
x = compression the spring = 6.5 cm = 6.5 cm (1 m /100 cm) = 0.065 m
the kinetic energy of box just before colliding with the spring converts into the spring energy of the spring when it is fully compressed.
Using conservation of energy
Kinetic energy of spring before collision = spring energy of spring after compression
(0.5) m v² = (0.5) k x²
m v² = k x²
inserting the values
(3.5 kg) v² = (85 N/m) (0.065 m)²
v = 0.32 m/s
Answer: 
Explanation:
According to the described situation we have the following data:
Horizontal distance between lily pads: 
Ferdinand's initial velocity: 
Time it takes a jump: 
We need to find the angle 
at which Ferdinand jumps.
In order to do this, we first have to find the <u>horizontal component (or x-component)</u> of this initial velocity. Since we are dealing with parabolic movement, where velocity has x-component and y-component, and in this case we will choose the x-component to find the angle:
(1)
(2)
(3)
On the other hand, the x-component of the velocity is expressed as:
(4)
Substituting (3) in (4):
(5)
Clearing :
This is the angle at which Ferdinand the frog jumps between lily pads
Here if we consider bullet and gun as a system then we can say that momentum of the system will remain conserved
so we will have
now we know that
now we will have
so gun will recoil with speed 6.67 m/s
