A spring has a force constant of 70000 N/m.

How far must it be stretched for its potential energy to be 21 J?

well, let's see. You are only given two pieces of data, so the manipulation must be simple.

energy(N-m) = N/m * m^2

P.E. = 1/2 kx^2
21 = 1/2 (70000)x^2
x^2 = .0006
x = .0245m or 2.45 cm

Well, you know what they say – if you want to find the potential energy of a spring, you have to spring into action! Now, let's calculate this together.

The formula for potential energy of a spring is given by the equation:

PE = 1/2 * k * x^2

Where PE is the potential energy, k is the force constant, and x is the displacement or stretch of the spring.

Now, plug in the values you provided. You want the potential energy to be 21 J, and the force constant is 70000 N/m. Let's solve for x:

21 J = 1/2 * 70000 N/m * x^2

Now, let's simplify and solve for x:

42 = 70000 * x^2

Dividing both sides by 70000:

x^2 = 42 / 70000

And then by taking the square root:

x = √(42 / 70000)

Calculating this should give you the answer you're looking for.

To find the distance the spring must be stretched, we can use the formula for potential energy stored in a spring.

The formula for potential energy stored in a spring is given by:

PE = (1/2) * k * x^2

Where:
PE = Potential Energy stored in the spring (in Joules)
k = Force constant of the spring (in Newtons per meter, N/m)
x = displacement or stretch of the spring from its equilibrium position (in meters)

Given:
PE = 21 J
k = 70000 N/m

We can rearrange the formula to solve for x:

PE = (1/2) * k * x^2

x^2 = (2 * PE) / k

x = √[(2 * PE) / k]

Plugging in the given values:

x = √[(2 * 21) / 70000]

x = √[0.0006]

x ≈ 0.0245 meters

Therefore, the spring must be stretched approximately 0.0245 meters for its potential energy to be 21 J.

To find the distance the spring must be stretched, we can use the formula for potential energy stored in a spring:

Potential Energy (PE) = 1/2 * k * x^2

Where:
- PE is the potential energy stored in the spring (given as 21 J)
- k is the force constant of the spring (given as 70000 N/m)
- x is the distance the spring is stretched (unknown)

We can rearrange the formula to solve for x:

x = sqrt((2 * PE) / k)

Let's plug in the values and calculate:

x = sqrt((2 * 21 J) / 70000 N/m)
x = sqrt(42 J / 70000 N/m)
x ≈ sqrt(6.000e-4 m)
x ≈ 0.0245 m

Therefore, the spring must be stretched approximately 0.0245 meters for its potential energy to be 21 J.