A 0.473 kg mass is attached to a spring with a spring constant 110 N/m so that the mass is allowed to move on a horizontal frictionless surface. The mass is released from rest when the spring is compressed 0.119 m.
Find the maximum force on the mass.
F = 0.119m * 110N./m =
To find the maximum force on the mass, we need to consider the restoring force of the spring when it is fully stretched or compressed.
The restoring force of a spring can be determined by Hooke's Law, which states that the force is proportional to the displacement from the equilibrium position.
The equation for Hooke's Law is given as:
F = -kx
Where:
F = Restoring force of the spring
k = Spring constant
x = Displacement from the equilibrium position
In this case, the mass is released from rest when the spring is compressed 0.119 m. The displacement, x, is negative because the spring is compressed.
Given:
Mass (m) = 0.473 kg
Spring constant (k) = 110 N/m
Displacement (x) = -0.119 m
Using Hooke's Law, we can calculate the maximum force on the mass:
F = -kx
F = -(110 N/m)(-0.119 m)
F = 13.09 N
Therefore, the maximum force on the mass is 13.09 N.
To find the maximum force on the mass, we need to consider the relationship between the force exerted by the spring and the displacement of the mass.
The force exerted by a spring is given by Hooke's Law, which states that the force (F) exerted by a spring is directly proportional to the displacement (x) from its equilibrium position and the spring constant (k). Mathematically, this can be expressed as:
F = -kx
where F is the force in Newtons (N), k is the spring constant in Newtons per meter (N/m), and x is the displacement from the equilibrium position in meters (m).
In this case, the spring constant (k) is given as 110 N/m and the displacement (x) is given as 0.119 m. Plugging in these values, we can calculate the force exerted by the spring:
F = -kx
F = -(110 N/m)(0.119 m)
F = -13.09 N
The negative sign indicates that the force exerted by the spring is in the opposite direction to the displacement.
Therefore, the maximum force on the mass is 13.09 N.
To find this answer, you can use the formula for the force exerted by a spring, which states that the force (F) is equal to the product of the spring constant (k) and the displacement (x) from the equilibrium position. In this case, the given values allow us to compute the maximum force on the mass using this formula.