A spring stretches by 6cm when supporting a load of 15N (a) how much would it stretch when supporting a load of 5kg
x/5g = 5/15
5
To find out how much the spring would stretch when supporting a load of 5 kg, we first need to convert the load from kilograms to newtons.
The weight of an object can be calculated by multiplying its mass (in kg) by the acceleration due to gravity, which is approximately 9.8 m/s^2.
So, to convert 5 kg to newtons, we use the formula:
Weight (in newtons) = mass (in kg) x acceleration due to gravity.
Weight = 5 kg x 9.8 m/s^2 = 49 N.
Now, we can use the information given that the spring stretches by 6 cm (0.06 m) when supporting a load of 15 N.
We can set up a ratio to determine the stretch of the spring when supporting a load of 49 N:
(initial load)/(initial stretch) = (new load)/(new stretch)
15 N / 0.06 m = 49 N / x
Solving for x, the new stretch of the spring:
x = (49 N / 15 N) * 0.06 m
x = 0.196 m.
Therefore, the spring would stretch approximately 0.196 m (or 19.6 cm) when supporting a load of 5 kg.
To find out how much a spring would stretch when supporting a load of 5kg, we need to know the spring constant (k) of the spring.
The spring constant is a measure of the stiffness of the spring and is denoted by the symbol k. It is usually represented in units of Newton per meter (N/m).
Given that the spring stretches by 6cm (or 0.06m) when supporting a load of 15N, we can use this information to calculate the spring constant.
The formula to calculate the spring constant is:
k = F / x
where k is the spring constant, F is the force applied to the spring, and x is the displacement (change in length) of the spring.
Using the given values, we can substitute them into the formula:
k = 15 N / 0.06 m
Simplifying the equation:
k = 250 N/m
Now that we have the spring constant, we can use it to determine how much the spring would stretch when supporting a load of 5kg.
First, do the conversion from 5kg to Newton:
1 kg = 9.8 N
So, 5kg = 5 * 9.8 N = 49 N
Now, we can use the formula:
F = k * x
Rearranging the formula to solve for x:
x = F / k
Plugging in the values:
x = 49 N / 250 N/m
Simplifying the equation:
x = 0.196 m
Therefore, the spring would stretch by approximately 0.196 meters (or 19.6 cm) when supporting a load of 5kg.