A certain spring stretches 5.3 cm when it
supports a mass of 0.65 kg .
If the elastic limit is not reached, how far
will it stretch when it supports a mass of
10 kg ? Answer in cm
Well, if 0.65 kg makes it stretch 5.3 cm, then 10 kg should make it stretch... my patience! Just kidding! Let's do some math, shall we?
We can use Hooke's Law to solve this problem. Hooke's Law states that the stretch of a spring is directly proportional to the force applied to it.
So, if we have a mass of 0.65 kg that stretches the spring by 5.3 cm, we can set up a proportion to find out how far a 10 kg mass will stretch it.
(0.65 kg)/(10 kg) = (5.3 cm)/(x)
Cross multiplying, we get:
0.65 kg * x = 10 kg * 5.3 cm
Simplifying, we find:
0.65x = 53 cm
Finally, dividing both sides by 0.65, we get:
x = 81.54 cm
Therefore, the spring will stretch approximately 81.54 cm when supporting a mass of 10 kg. But you know, the spring might throw a surprise party and stretch a bit more just to keep things interesting!
To find how far the spring will stretch when it supports a mass of 10 kg, we can use Hooke's law, which states that the force applied to a spring is proportional to the extension or compression of the spring.
According to Hooke's law, the force applied to the spring is given by:
F = k * x
Where:
F is the force applied to the spring (in Newtons),
k is the spring constant (in N/m), and
x is the extension or compression of the spring (in meters).
We are given that the spring stretches 5.3 cm (which is equivalent to 0.053 m) when it supports a mass of 0.65 kg. This information can help us find the spring constant.
The force applied to the spring is equal to the weight of the mass, which can be calculated using:
F = m * g
Where:
F is the force applied to the spring (in Newtons),
m is the mass (in kg), and
g is the acceleration due to gravity (approximately 9.8 m/s^2).
Substituting the given values:
F = 0.65 kg * 9.8 m/s^2 = 6.37 N
Using Hooke's law, we can rearrange the equation to solve for the spring constant:
k = F / x
Substituting the values:
k = 6.37 N / 0.053 m = 120.19 N/m
Now, we need to calculate how far the spring will stretch when it supports a mass of 10 kg:
Using Hooke's law:
F = k * x
Substituting the known values:
10 kg * 9.8 m/s^2 = 120.19 N/m * x
Simplifying the equation:
98 N = 120.19 N/m * x
Dividing both sides of the equation by 120.19 N/m:
x = 98 N / 120.19 N/m
Calculating the value of x:
x ≈ 0.815 m
Converting the value of x from meters to centimeters:
x ≈ 0.815 m * 100 cm/m = 81.5 cm
Therefore, the spring will stretch approximately 81.5 cm when it supports a mass of 10 kg.
To calculate how far the spring will stretch when it supports a mass of 10 kg, we need to use Hooke's Law. Hooke's Law states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
The formula for Hooke's Law is: F = kx
Where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the spring.
In this case, we are given the displacement of the spring when it supports a mass of 0.65 kg, which is 5.3 cm. We can use this information to find the spring constant, k.
The force exerted on the spring can be calculated using the equation: F = mg
Where m is the mass supported by the spring and g is the acceleration due to gravity (approximately 9.8 m/s^2).
So, when the spring supports a mass of 0.65 kg, the force exerted on the spring is: F = (0.65 kg)(9.8 m/s^2) = 6.37 N
Using Hooke's Law, we can find the spring constant, k:
6.37 N = k(5.3 cm)
Converting the displacement to meters: 5.3 cm = 0.053 m
Now we can solve for k:
k = 6.37 N / 0.053 m = 120.19 N/m
Now that we have the spring constant, we can use Hooke's Law to find the displacement of the spring when it supports a mass of 10 kg.
F = kx
10 kg * 9.8 m/s^2 = 120.19 N/m * x
98 N = 120.19 N/m * x
Dividing both sides by 120.19 N/m:
x = 98 N / 120.19 N/m = 0.814 m
Converting the displacement to centimeters:
x = 0.814 m * 100 cm/m = 81.4 cm
Therefore, the spring will stretch approximately 81.4 cm when it supports a mass of 10 kg.
Deflection will be proportional to the weight applies (Hooke's Law).
X = Deflection = k * mass
X2/X1 = M2/M1
X2 = (M2/M1)*X1
Multiply 5.3 cm by 10/0.65 for the answer.