A certain spring stretches 4.4 cm when it
supports a mass of 0.89 kg .
If the elastic limit is not reached, how far
will it stretch when it supports a mass of
10 kg ?
Answer in units of cm.
d = 4.4cm/0.89kg * 10kg =
Well, it sounds like this spring has been working out! Now it's time to flex its elasticity muscles.
Let's do a little math workout. We know that when the spring supports a mass of 0.89 kg, it stretches by 4.4 cm. So, we can call this our "spring stretch rate": 4.4 cm / 0.89 kg.
Now, if we want to find out how far the spring will stretch when supporting a mass of 10 kg, we can use our spring stretch rate. We'll calculate it like this:
spring stretch rate = spring stretch / mass
Let's plug in the values:
spring stretch rate = 4.4 cm / 0.89 kg
Now, we can rearrange the equation to solve for the spring stretch when supporting a mass of 10 kg:
spring stretch = spring stretch rate * mass
spring stretch = (4.4 cm / 0.89 kg) * 10 kg
Calculating this, we get:
spring stretch = 4.4 cm / 0.89 * 10
spring stretch ≈ 49.4 cm
So, when the spring supports a 10 kg mass, it will stretch approximately 49.4 cm. That's really stretching it, huh? Just imagine how much the spring must be longing for a relaxing vacation!
The distance a spring stretches is directly proportional to the mass it supports. This relationship is given by Hooke's Law: F = -kx, where F is the force applied to the spring, k is the spring constant, and x is the distance the spring stretches.
To find the spring constant, we can rearrange Hooke's Law to solve for k: k = -F/x.
Given that the spring stretches 4.4 cm when it supports a mass of 0.89 kg, we can use this information to find the spring constant:
4.4 cm = x
0.89 kg = = -F/x = -(0.89 kg)/(4.4 cm)
Now, we can use the spring constant to find how far the spring will stretch when it supports a mass of 10 kg:
x = -F/k = -(10 kg)/(k)
Substituting the value of k, we have:
x = -(10 kg)/(-(0.89 kg)/(4.4 cm))
Simplifying further:
x = (10 kg) * (4.4 cm)/(0.89 kg)
Calculating this expression:
x ≈ 49.438 cm
Therefore, the spring will stretch approximately 49.438 cm when it supports a mass of 10 kg.
To find how far the spring will stretch when supporting a mass of 10 kg, we need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to the amount it stretches or compresses. Mathematically, it can be expressed as:
F = k * x
Where F is the force applied on the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position.
In this case, we know that when the spring supports a mass of 0.89 kg, it stretches 4.4 cm. We can use this information to calculate the spring constant, k.
Step 1: Calculate the force applied on the spring
Given that the mass is 0.89 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can find the force using Newton's second law:
Force = mass * acceleration
F = 0.89 kg * 9.8 m/s^2
Step 2: Convert the force to Newtons
The force obtained in step 1 is in kg*m/s^2. Since the spring constant is typically expressed in N/m, we need to convert the force to Newtons:
1 N = 1 kg*m/s^2
F in N = F in kg*m/s^2 / 1
Step 3: Calculate the spring constant
Using Hooke's Law (F = k * x) and rearranging the formula, we can solve for the spring constant (k):
k = F / x
Given that F is the force calculated in step 2, and x is the displacement of the spring (4.4 cm or 0.044 m), we can substitute these values to find k.
Step 4: Calculate the displacement for a mass of 10 kg
Once we have the spring constant (k), we can use Hooke's Law to find the displacement (x) for a mass of 10 kg:
F = k * x
x = F / k
Given that the mass is now 10 kg, we can calculate the force using Newton's second law:
Force = mass * acceleration
F = 10 kg * 9.8 m/s^2
Substituting the mass and force values into the equation, we can calculate the displacement (x) for a mass of 10 kg.
Remember to convert the displacement back to cm for the final answer.
By following these steps, you should be able to find how far the spring will stretch when it supports a mass of 10 kg.