A board rests on two springs, keeping the springs at equilibrium. Each spring has a spring constant of 10,000 N/m. How far will each spring compress when a 50kg person sits on the board?
Any idea how to do this?
Well, let's spring into action and figure it out! To solve this problem, we'll use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement or compression of the spring.
First, we need to determine the total force exerted by the person on the board. We can do this by multiplying the person's weight (mass * acceleration due to gravity) by the gravitational constant, which is approximately 9.8 m/s².
So, the total force exerted is:
Force = mass * acceleration due to gravity
Force = 50 kg * 9.8 m/s²
Force = 490 N
Next, we can calculate the compression of each spring. Since we have two identical springs in parallel, the force will be evenly distributed between them.
For a spring obeying Hooke's Law, the force exerted is given by:
Force = spring constant * displacement
Therefore, the displacement of each spring is:
Displacement = Force / spring constant
Displacement = 490 N / 10,000 N/m
Displacement = 0.049 m
So, each spring will compress by approximately 0.049 meters when the person sits on the board. That's quite a springy situation!
To solve this problem, you 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.
Step 1: Calculate the gravitational force acting on the person.
The gravitational force (Fg) is given by the equation Fg = m * g, where m is the mass of the person and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Fg = 50 kg * 9.8 m/s^2
Fg = 490 N
Step 2: Calculate the total force exerted by both springs.
Since the board is at equilibrium, the total force exerted by the springs (Fs) is equal to the gravitational force.
Fs = Fg
Fs = 490 N
Step 3: Calculate the compression of each spring using Hooke's Law.
Hooke's Law states that Fs = k * x, where k is the spring constant and x is the displacement or compression of the spring.
Since there are two springs, the total compression of both springs (x_total) is equal to the compression of each individual spring (x) multiplied by 2.
Fs = 2 * k * x
490 N = 2 * (10,000 N/m) * x
Step 4: Solve for x, the compression of each spring.
x = 490 N / (2 * 10,000 N/m)
x = 0.0245 meters or 24.5 mm
Therefore, each spring will compress approximately 0.0245 meters (or 24.5 mm) when a 50 kg person sits on the board.
To find out how far each spring will compress when a 50kg person sits on the board, we can use Hooke's Law. Hooke's Law states that the force exerted by a spring is directly proportional to the displacement or compression of the spring.
Let's start by calculating the weight of the person. The weight is equal to the mass multiplied by the acceleration due to gravity, which is approximately 9.8 m/s^2.
Weight = mass * acceleration due to gravity
Weight = 50kg * 9.8 m/s^2
Weight = 490N
Since there are two identical springs supporting the board, each spring will need to support half of the weight of the person, which is 245N.
Now, we can apply Hooke's Law to determine the compression of each spring. Hooke's Law equation is given as:
Force = spring constant * compression
Since the force exerted by each spring is 245N and the spring constant is 10,000 N/m, the compression of each spring can be calculated as follows:
245N = 10,000 N/m * compression
Rearranging the equation to isolate the compression:
compression = Force / spring constant
compression = 245N / 10,000 N/m
compression = 0.0245 m = 24.5 mm
Therefore, each spring will compress by 0.0245 meters (or 24.5 millimeters) when a 50kg person sits on the board.
depends on where on the board the person sits
if they sit at the center, then the springs compress equally
... the person's weight is 50 g ... 490 N
... so, 245 N on each spring
245 N / (10k N/m) = ? m