Have you heard an ambulance, police car, or fire truck recently? Did you notice that the pitch of the siren changed as it approa
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Answer:
final velocity = 0.08585m/s
Explanation:
We are taking train cars as our system. In this system no external force is acting. So we can apply the law of conservation of linear momentum.
The law of conservation of linear momentum states that the total linear momentum of a system remains constant if there is no external force acting on the system. That is total linear momentum before = total linear momentum after
total linear momentum before = linear momentum of first train car + linear momentum of second train car
We know that linear momentum = mv
where,
m = mass
v = velocity
thus,
total linear momentum before = m₁v₁ + m₂v₂
m₁ = mass of first train car = 135,000kg
v₁ = velocity of first train car = 0.305m/s
m₂ = mass of first second car = 100,000kg
v₂ = velocity of second train car = −0.210m/s
Note: Momentum is a vector. So while adding momentum we should take account of its direction too. Here since second train car is moving in a direction opposite to that of the first one, we have taken its velocity as negative.
total linear momentum before = m₁v₁ + m₂v₂
= 135,000x0.305 + 100,000x(−0.210)
= 135,000x0.305 - 100,000x0.210
= 20,175 kgm/s
Now we have to find total linear momentum after bumping. After the bumping both the train cars will be moving together with a common velocity(say v).
Therefore, total linear momentum after = mv
m = m₁ + m₂ = 135,000 + 100,000 = 235,000
total linear momentum before = total linear momentum after
235,000v = 20,175
v =
= 0.08585m/s
Answer:
<em>Both energies are equal when the rock has fallen 20 m or equivalently when it is at a height of 20 m.</em>
Explanation:
<u>Potential and Kinetic Energy</u>
The gravitational potential energy is the energy an object has due to its height above the ground. The formula is
Where:
m = mass of the object
g = acceleration of gravity (9.8~m/s^2)
h = height
Note we can also use the object's weight W=mg into the formula:
The kinetic energy is the energy an object has due to its speed:
Where v is the object's speed.
Initially, the object has no kinetic energy because it's assumed at rest.
The W=30 N rock falls from a height of h=40 m, thus:
Since the sum of the kinetic and potential energies is constant:
U' + K' = 1,200 J
Here, U' and K' are the energies at any point of the motion. Since both must be the same:
U' = K' = 600 J
U'=Wh'=600
Solving for h':
Both energies are equal when the rock has fallen 20 m or equivalently when it is at a height of 20 m.
Answer:
The velocity of motion at which the occupants of the car appear to weigh 20% less than their normal weight is approximately 19.81 m/s
Explanation:
The given parameters are;
The curvature of the hill, r = 200 m
Due to the velocity, v, the occupants weight = 20% less than the normal weight
The outward force of an object due to centripetal (motion) force is given by the following equation;
Where;
r = The radius of curvature of the hill = 200 m
Given that the weight of the occupants, W = m × g, we have;
v = √(0.2 × g × r)
By substitution, we have;
v = √(0.2 × 9.81 × 200) ≈ 19.81
The velocity of motion at which the occupants of the car appear to weigh 20% less than their normal weight ≈ 19.81 m/s.