A 2.60-kg block is attached to a horizontal spring that has a spring constant of 214 N/m. At the instant when the displacement of the spring from its unstrained length is -0.115 m, what is the acceleration a of the object? In your answer, be sure to include the proper plus or minus sign.
The force that the spring exerts
F=-kx=ma
a=-k(-.115)/2.60 so compute
To find the acceleration of the object, we can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position.
The equation for Hooke's Law is given by:
F = -k * x
Where:
F is the force exerted by the spring,
k is the spring constant, and
x is the displacement from the equilibrium position.
In this problem, the block is attached to a horizontal spring, so the force exerted by the spring will cause the block to accelerate.
Given:
Mass of the block, m = 2.60 kg
Spring constant, k = 214 N/m
Displacement of the spring, x = -0.115 m
To find the acceleration, we need to find the force exerted by the spring.
Using Hooke's Law, we can write:
F = -k * x
Substituting the given values:
F = -214 N/m * (-0.115 m)
F = 24.61 N
Now, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass times its acceleration.
F = m * a
Rearranging the equation:
a = F / m
Substituting the given values:
a = 24.61 N / 2.60 kg
a = 9.47 m/s²
Therefore, the acceleration of the object is 9.47 m/s².
To find the acceleration of the object, we need to use Hooke's law, which states that the force exerted by a spring is proportional to the displacement of the spring from its original position. The formula for Hooke's law is:
F = -kx
Where:
F = Force applied by the spring
k = Spring constant
x = Displacement from the equilibrium position
First, let's calculate the force exerted by the spring using Hooke's law. Given that the spring constant (k) is 214 N/m and the displacement (x) is -0.115 m:
F = - (214 N/m) * (-0.115 m)
F = 24.61 N
Since we know the mass of the block (2.60 kg), we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = ma
Rearranging the formula, we can solve for acceleration (a):
a = F / m
Plugging in the values, we get:
a = (24.61 N) / (2.60 kg)
a ≈ 9.466 m/s²
Therefore, the acceleration of the object is approximately 9.466 m/s².