A string stretches by 6cm when supporting a load of 15N.By how much would it stretch when supporting a load of 5kg
To solve this problem, we need to first convert the load from kilograms (kg) to Newtons (N). We know that 1 kg is equal to 9.8 N.
Given that the string stretches by 6 cm when supporting a load of 15 N, we can set up a proportion to find out how much it would stretch when supporting a load of 5 kg.
Let's denote the amount of stretch when supporting a load of 5 kg as 'x' cm.
Using the proportional relationship, we can set up the following equation:
15 N / 6 cm = 5 kg / x cm
Now we can solve for x.
First, convert 5 kg to Newtons:
5 kg * 9.8 N/kg = 49 N
Now we have:
15 N / 6 cm = 49 N / x cm
Cross-multiplying, we get:
15 N * x cm = 49 N * 6 cm
Dividing both sides by 15 N, we get:
x cm = (49 N * 6 cm) / 15 N
Simplifying, we have:
x cm = 294 cm / 15
Dividing, we find that:
x cm ≈ 19.6 cm
Therefore, the string would stretch by approximately 19.6 cm when supporting a load of 5 kg.
since F=kx, you want x such that
15/6 = (5*9.81)/x
To find out how much the string would stretch when supporting a load of 5kg, we can use the concept of proportionality. The stretch of the string is directly proportional to the load applied.
Given that the string stretches by 6cm when supporting a load of 15N, we can set up a proportion to solve for the stretch when supporting a load of 5kg.
First, convert the load of 5kg to Newtons. 1 kg is equal to 9.8 Newtons, so 5 kg is equal to 5 x 9.8 = 49 Newtons.
Let x be the stretch of the string when supporting a load of 49N.
We can set up the following proportion:
6 cm / 15 N = x cm / 49 N
To solve for x, we can cross-multiply:
15 N * x cm = 6 cm * 49 N
Divide both sides of the equation by 15 N to isolate x:
x cm = (6 cm * 49 N) / 15 N
Simplifying the equation:
x cm = 294 cm / 15
x cm ≈ 19.6 cm
Therefore, the string would stretch by approximately 19.6 cm when supporting a load of 5kg.