The spring constant of the spring in the
figure is 25 N/m, and the mass of the object
is 4 kg. The spring is unstretched and the
surface is frictionless. A constant 18 N force is
applied horizontally to the object (stretching
the spring).
v0 = 0
Find the speed of the object after it has
moved a distance of 0.35 m.
Answer in units of m/s
the total energy is W+K=U
So it would be Fd+(.5*m*v^2)=.5*k*x^2
Plug in the numbers, 18*.35+.5*25*v^2=.5*25*.35^2
6.3+12.5*v^2=1.53125
v=sqrt0.3815 (ignore the negative)
v=0.61765m/s
To find the speed of the object after it has moved a distance of 0.35 m, we can use the principles of work, energy, and Hooke's law.
First, let's analyze the situation. The applied force of 18 N stretches the spring, which creates a restoring force opposing the displacement of the object. The spring force is given by Hooke's law as F = -kx, where F is the force, k is the spring constant, and x is the displacement.
The work done on the object by the applied force is equal to the change in the object's kinetic energy. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Therefore, we can write:
Work done = Change in kinetic energy
(18 N) * (0.35 m) = (1/2) * m * v^2
In this equation, m is the mass of the object, and v is the final velocity we want to find.
Now, let's plug in the given values. The mass of the object is 4 kg, and the spring constant is 25 N/m. We also know that the initial velocity (v0) is 0.
(18 N) * (0.35 m) = (1/2) * (4 kg) * v^2
Simplifying the equation:
6.3 N·m = 2 kg·v^2
Dividing both sides by 2 kg:
3.15 N·m/kg = v^2
Taking the square root of both sides:
√(3.15 N·m/kg) = v
Now, let's calculate the value:
v = √(3.15 N·m/kg) ≈ 1.77 m/s
Therefore, the speed of the object after it has moved a distance of 0.35 m is approximately 1.77 m/s.