a vertical spring whose spring constant is 850 n/m stands on a table and is compressed 0.400m. what speed can it give to a .300kg ball when released?
(u)potential energy stored in the spring=kx^2/2
(k.e)kinetic energy of the ball when released=1/2mv^2
u=k.e
kx^2/2=1/2mv^2
put all the known values
v=21.291625896895082665426993569307
To find the speed that the spring can give to the ball when released, we need to apply the principles of conservation of mechanical energy.
1. First, let's find the potential energy stored in the compressed spring.
The potential energy stored in a spring is given by the formula: PE = (1/2)kx²
Where:
- PE is the potential energy
- k is the spring constant
- x is the compression or extension of the spring from its equilibrium position
Plugging in the values: k = 850 N/m and x = 0.400 m
PE = (1/2) * 850 N/m * (0.400 m)²
PE = 68 J (joules)
2. The potential energy stored in the spring will be converted into the kinetic energy of the ball when the spring is released.
The kinetic energy of an object is given by the formula: KE = (1/2)mv²
Where:
- KE is the kinetic energy
- m is the mass of the object
- v is the velocity or speed of the object
We need to solve for v. Rearranging the formula:
v = √(2KE / m)
Since the potential energy is converted entirely into kinetic energy, KE = PE = 68 J.
Plugging in the values: m = 0.300 kg and KE = 68 J
v = √(2 * 68 J / 0.300 kg)
v ≈ 11.15 m/s (rounded to two decimal places)
Therefore, the speed that the spring can give to the 0.300 kg ball when released is approximately 11.15 m/s.
To find the speed that the spring can give to the ball when released, we can use the principles of potential and kinetic energy.
1. Calculate the potential energy stored in the spring when it is compressed:
- The potential energy can be calculated using the formula: PE = (1/2) * k * x^2
Where PE is the potential energy, k is the spring constant, and x is the compression distance.
- Given:
k = 850 N/m (spring constant)
x = 0.400 m (compression distance)
- Substitute the values into the formula:
PE = (1/2) * 850 N/m * (0.400 m)^2
PE = (1/2) * 850 N/m * 0.16 m^2
PE = 34 J (potential energy)
2. The potential energy stored in the spring is converted into kinetic energy when the ball is released. Therefore, the kinetic energy of the ball can be equal to the potential energy of the spring:
- The kinetic energy formula is given by: KE = (1/2) * m * v^2
Where KE is the kinetic energy, m is the mass of the ball, and v is the velocity of the ball.
- Given:
m = 0.300 kg (mass of the ball)
KE = PE (potential energy)
v = ? (velocity to be found)
- Substitute the values into the formula:
KE = (1/2) * 0.300 kg * v^2
34 J = (1/2) * 0.300 kg * v^2
34 J = 0.150 kg * v^2
3. Solve for the velocity (v):
- Rearrange the equation to solve for v:
v^2 = (34 J) / (0.150 kg)
- Take the square root of both sides to solve for v:
v = √(34 J / 0.150 kg)
- Calculate the velocity:
v ≈ 10.08 m/s
Therefore, when released, the spring can give the 0.300 kg ball a velocity of approximately 10.08 m/s.