A 0.30 kg mass is attached to a spring with a spring constant 170 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 0.15 m.
(a) Find the force on the mass.
N
(b) Find its acceleration at this instant
m/s2
To find the force on the mass, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement. The formula for Hooke's Law is:
F = -kx
where F is the force, k is the spring constant, and x is the displacement.
In this case, the spring constant is given as 170 N/m, and the displacement is given as 0.15 m. Plugging in these values into the formula, we get:
F = -(170 N/m)(0.15 m)
F = -25.5 N
Since the negative sign indicates that the force is in the opposite direction of the displacement, we can discard it and conclude that the force on the mass is 25.5 N (in the positive direction).
To find the acceleration of the mass at this instant, we can use Newton's second law, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula for Newton's second law is:
a = F/m
where a is the acceleration, F is the force, and m is the mass.
In this case, the force is 25.5 N and the mass is 0.30 kg. Plugging these values into the formula, we get:
a = (25.5 N)/(0.30 kg)
a ≈ 85 m/s²
Therefore, the acceleration of the mass at this instant is approximately 85 m/s².
To calculate the force on the mass, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
(a) The force on the mass can be calculated using the equation:
F = -kx
where F is the force in Newtons, k is the spring constant in N/m, and x is the displacement of the spring from its equilibrium position in meters.
Given:
k = 170 N/m
x = 0.15 m
Substituting the given values into the equation, we get:
F = -170 N/m * 0.15 m
F = -25.5 N
Therefore, the force on the mass is 25.5 N.
(b) To find the acceleration of the mass at this instant, we can use Newton's second law, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
F = ma
Given:
F = -25.5 N
m = 0.30 kg
Substituting the values into the equation, we get:
-25.5 N = 0.30 kg * a
a = -25.5 N / 0.30 kg
a ≈ -85 m/s^2
Therefore, the acceleration of the mass at this instant is approximately -85 m/s^2.