A 5 kg mass is thrown up with a velocity of 4 m/s from a height of 30 m onto a spring with a relaxed length of 10 m, and a constant of 400 N/m. What will the maximum compression of the spring be? What will the speed of the object be when the spring is compressed 0.3 m?
This looks like a duplicate post. I amswered it already
I think you have this question confused with this one:
A 200 N/m, 5 m spring on a 20 degree incline is compressed 2.3 m and a 5 kg block is placed on it. If we neglect friction, how far up the incline will the block travel? How fast will it be traveling when it is 0.2 m up the incline?
sofa wont fit through the door so i lift the 86.1 kg sofa 17.2 m from the street. how much time will the lift take?
To find the maximum compression of the spring, we need to consider the conservation of mechanical energy.
First, let's find the initial potential energy and initial kinetic energy of the object:
Initial potential energy (PEi) = mgh, where m is the mass (5 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the initial height (30 m).
PEi = 5 kg * 9.8 m/s^2 * 30 m = 1470 J
Initial kinetic energy (KEi) = 0.5 * m * v^2, where m is the mass (5 kg) and v is the initial velocity (4 m/s).
KEi = 0.5 * 5 kg * (4 m/s)^2 = 40 J
The initial mechanical energy (Ei) is the sum of the initial potential energy and the initial kinetic energy:
Ei = PEi + KEi = 1470 J + 40 J = 1510 J
When the object reaches its maximum compression, all its initial potential energy will be converted into potential energy stored in the compressed spring (PEs). Therefore, we can say:
PEs = PEi
The potential energy of the spring is given by:
PEs = 0.5 * k * x^2, where k is the spring constant (400 N/m) and x is the maximum compression of the spring.
Setting PEs equal to PEi, we get:
0.5 * k * x^2 = PEi
0.5 * 400 N/m * x^2 = 1510 J
200x^2 = 1510 J
x^2 = 1510 J / 200
x^2 = 7.55 m
Taking the square root of both sides, we find:
x ≈ sqrt(7.55) ≈ 2.75 m
Therefore, the maximum compression of the spring will be approximately 2.75 meters.
To find the speed of the object when the spring is compressed 0.3 m, we will use the principle of conservation of mechanical energy again.
The final potential energy stored in the compressed spring (PEf) is given by:
PEf = 0.5 * k * x^2, where k is the spring constant (400 N/m) and x is the compression of the spring (0.3 m).
PEf = 0.5 * 400 N/m * (0.3 m)^2 = 18 J
Since mechanical energy is conserved, the final kinetic energy (KEf) will be equal to the initial mechanical energy (Ei). Therefore:
KEf = Ei - PEf = 1510 J - 18 J = 1492 J
The final kinetic energy (KEf) is given by:
KEf = 0.5 * m * v^2, where m is the mass (5 kg) and v is the final velocity we want to find.
Plugging in the values, we get:
1492 J = 0.5 * 5 kg * v^2
v^2 = 1492 J / 2.5 kg
v^2 = 596.8 m^2/s^2
Taking the square root of both sides, we get:
v ≈ sqrt(596.8) ≈ 24.43 m/s
Therefore, the speed of the object when the spring is compressed 0.3 m will be approximately 24.43 m/s.