A spring lies on a horizontal table, and the left end of the spring is attached to a wall. The other end is connected to a box. The box is pulled to the right, stretching the spring. Static friction exists between the box and the table, so when the spring is stretched only by a small amount and the box is released, the box does not move. The mass of the box is 0.85 kg, and the spring has a spring constant of 77 N/m. The coefficient of static friction between the box and the table on which it rests is μs = 0.60. How far can the spring be stretched from its unstrained position without the box moving when it is released?
No ... it's spelled physics.
I think maybe spelled Physics.
However it is an obvious case of homework or quiz dumping and does not interest me. At least one of the problems is in every beginning physics text. The student has not tried.
To determine how far the spring can be stretched without the box moving when it is released, we need to find the maximum force of static friction between the box and the table. This force must be equal to or larger than the force exerted by the spring.
The force exerted by the spring can be calculated using Hooke's Law, which states that the force exerted by a spring is proportional to its displacement. The formula is:
F = k * x
Where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the unstrained position.
So, to find the maximum force of static friction, we need to set up an equation equating the force of static friction to the force of the spring:
μs * m * g = k * x
Where μs is the coefficient of static friction, m is the mass of the box, g is the acceleration due to gravity, k is the spring constant, and x is the displacement.
Now, we can rearrange the equation to solve for x:
x = (μs * m * g) / k
Plugging in the given values:
μs = 0.60
m = 0.85 kg
g = 9.8 m/s^2
k = 77 N/m
x = (0.60 * 0.85 kg * 9.8 m/s^2) / 77 N/m
Calculating this gives:
x ≈ 0.086 meters or 8.6 cm
Therefore, the spring can be stretched by approximately 8.6 cm from its unstrained position without causing the box to move when it is released.