(a) To find the spring constant (k), we can use Hooke's Law, which states that the force exerted by a spring is equal to the displacement from the equilibrium position multiplied by the spring constant. The formula is F = kx.

First, we need to find the displacement (x). The spring was initially 38.0 cm long and stretched to 41.0 cm, so the displacement is 41.0 cm - 38.0 cm = 3.0 cm. We need to convert this to meters, so x = 3.0 cm * (1 m/100 cm) = 0.03 m.

The force (F) exerted on the spring is equal to the weight of the 8.00-kg object, which is mass times gravity. So, F = m*g = 8.00 kg * 9.8 m/s^2 = 78.4 N.

Now we can find the spring constant using the formula k = F/x = 78.4 N / 0.03 m = 2613.33 N/m or 2.613 kN/m.

(b) When two people pull the spring with a force of 170 N each, the total force on the spring is 2*170 N = 340 N.

We can find the new displacement of the spring using the formula x = F/k. Substituting the values we have, x = 340 N / 2613.33 N/m = 0.13 m.

To find the new length of the spring, we add this displacement to the original length of the spring. The original length was 38.0 cm, which is 0.38 m. So, the new length is 0.38 m + 0.13 m = 0.51 m or 51.0 cm.

Question

(a) To find the spring constant (k), we can use Hooke's Law, which states that the force exerted by a spring is equal to the displacement from the equilibrium position multiplied by the spring constant. The formula is F = kx.

First, we need to find the displacement (x). The spring was initially 38.0 cm long and stretched to 41.0 cm, so the displacement is 41.0 cm - 38.0 cm = 3.0 cm. We need to convert this to meters, so x = 3.0 cm * (1 m/100 cm) = 0.03 m.

The force (F) exerted on the spring is equal to the weight of the 8.00-kg object, which is mass times gravity. So, F = m*g = 8.00 kg * 9.8 m/s^2 = 78.4 N.

Now we can find the spring constant using the formula k = F/x = 78.4 N / 0.03 m = 2613.33 N/m or 2.613 kN/m.

(b) When two people pull the spring with a force of 170 N each, the total force on the spring is 2*170 N = 340 N.

We can find the new displacement of the spring using the formula x = F/k. Substituting the values we have, x = 340 N / 2613.33 N/m = 0.13 m.

To find the new length of the spring, we add this displacement to the original length of the spring. The original length was 38.0 cm, which is 0.38 m. So, the new length is 0.38 m + 0.13 m = 0.51 m or 51.0 cm.

Knowee AI · Accepted Answer

(a) To find the spring constant (k), we can use Hooke's Law, which states that the force exerted by a spring is equal to the displacement from the equilibrium position multiplied by the spring constant. The formula is F = kx.

First, we need to find the displacement (x). The spring was initially 38.0 cm long and stretched to 41.0 cm, so the displacement is 41.0 cm - 38.0 cm = 3.0 cm. We need to convert this to meters, so x = 3.0 cm * (1 m/100 cm) = 0.03 m.

The force (F) exerted on the spring is equal to the weight of the 8.00-kg object, which is mass times gravity. So, F = m*g = 8.00 kg * 9.8 m/s^2 = 78.4 N.

Now we can find the spring constant using the formula k = F/x = 78.4 N / 0.03 m = 2613.33 N/m or 2.613 kN/m.

(b) When two people pull the spring with a force of 170 N each, the total force on the spring is 2*170 N = 340 N.

We can find the new displacement of the spring using the formula x = F/k. Substituting the values we have, x = 340 N / 2613.33 N/m = 0.13 m.

To find the new length of the spring, we add this displacement to the original length of the spring. The original length was 38.0 cm, which is 0.38 m. So, the new length is 0.38 m + 0.13 m = 0.51 m or 51.0 cm.

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