How far was the spring stretched from its unstreched length?
A mass m = 10 kg rests on a frictionless table and accelerated by a spring with spring constant k = 4777 N/m. The floor is frictionless except for a rough patch. For this rough path, the coefficient of friction is μk = 0.43. The mass leaves the spring at a speed v = 3.8 m/s.
so I got .17... but it's not correct, I used 3.8 sqrt(10/4777)
what am I doing wrng?
1/2 k x^2 = 1/2 m v^2 ... x = v √(m / k) ... x = 3.8 √(10 / 4777)
significant figures are the only thing that comes to mind
... the mass is one sig fig ... so the result should be also
To calculate the distance the spring was stretched from its unstretched length, you can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The formula to calculate this displacement is:
Δx = (mv) / k
where:
Δx = displacement of the spring
m = mass of the object (10 kg)
v = velocity of the object (3.8 m/s)
k = spring constant (4777 N/m)
Plugging in the values into the formula, we get:
Δx = (10 kg * 3.8 m/s) / 4777 N/m
Δx ≈ 0.00793 m (rounded to 5 decimal places)
Therefore, the spring was stretched approximately 0.00793 meters from its unstretched length.
To find the distance the spring was stretched from its unstretched length, we need to use the conservation of mechanical energy. The initial potential energy stored in the spring is equal to the final kinetic energy of the mass.
The initial potential energy stored in the spring is given by the equation:
Potential energy = (1/2)kx^2
where k is the spring constant and x is the distance the spring is stretched from its unstretched length.
The final kinetic energy of the mass is given by the equation:
Kinetic energy = (1/2)mv^2
where m is the mass of the object and v is the final speed.
Since energy is conserved, we can equate the initial potential energy to the final kinetic energy:
(1/2)kx^2 = (1/2)mv^2
Rearranging the equation, we get:
x^2 = (mv^2) / k
Plugging in the given values:
m = 10 kg
v = 3.8 m/s
k = 4777 N/m
x^2 = (10 * 3.8^2) / 4777
x^2 ≈ 3.01
Taking the square root of both sides yields:
x ≈ √(3.01)
x ≈ 1.73 m
Therefore, the distance the spring was stretched from its unstretched length is approximately 1.73 meters.
It seems that you have made an error in your calculation. Instead, try using the correct formula as shown above to get the accurate result.