When a 4.00 kg object is hung vertically on a certain light spring that obeys Hooke’s law, the spring stretches 2.50 cm. If the 4.00 kg object is removed:

(a) To find out how far the spring will stretch if a 1.50 kg block is hung on it, we can use the principle of proportionality in 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.

Let's denote the displacement of the spring when the 1.50 kg block is hung on it as x. We can set up the following proportion:

(4.00 kg)/(2.50 cm) = (1.50 kg)/x

Cross-multiplying and solving for x, we get:

x = (1.50 kg) * (2.50 cm) / (4.00 kg)
x = 0.9375 cm

Therefore, the spring will stretch 0.9375 cm when the 1.50 kg block is hung on it.

(b) To calculate the work required to stretch the same spring 4.00 cm from its unstretched position, we can use the formula for work done by a spring:

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

Where k is the spring constant and x is the displacement of the spring.

Since the spring obeys Hooke's law, we can use the given information to find the spring constant. Hooke's law states that the force exerted by a spring is equal to the spring constant multiplied by the displacement of the spring.

The force exerted by the 4.00 kg object is given by:

Force = mass * acceleration
Force = (4.00 kg) * (9.8 m/s^2)
Force = 39.2 N

According to Hooke's law, this force is equal to the spring constant multiplied by the displacement of the spring:

39.2 N = k * (2.50 cm)

Solving for k, we get:

k = 39.2 N / (2.50 cm)
k = 15.68 N/cm

Now we can calculate the work done to stretch the spring 4.00 cm:

Work = (1/2) * (15.68 N/cm) * (4.00 cm)^2
Work = 125.44 N*cm

Therefore, the external agent must do 125.44 N*cm of work to stretch the same spring 4.00 cm from its unstretched position.

Question

When a 4.00 kg object is hung vertically on a certain light spring that obeys Hooke’s law, the spring stretches 2.50 cm. If the 4.00 kg object is removed:

(a) To find out how far the spring will stretch if a 1.50 kg block is hung on it, we can use the principle of proportionality in 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.

Let's denote the displacement of the spring when the 1.50 kg block is hung on it as x. We can set up the following proportion:

(4.00 kg)/(2.50 cm) = (1.50 kg)/x

Cross-multiplying and solving for x, we get:

x = (1.50 kg) * (2.50 cm) / (4.00 kg)
x = 0.9375 cm

Therefore, the spring will stretch 0.9375 cm when the 1.50 kg block is hung on it.

(b) To calculate the work required to stretch the same spring 4.00 cm from its unstretched position, we can use the formula for work done by a spring:

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

Where k is the spring constant and x is the displacement of the spring.

Since the spring obeys Hooke's law, we can use the given information to find the spring constant. Hooke's law states that the force exerted by a spring is equal to the spring constant multiplied by the displacement of the spring.

The force exerted by the 4.00 kg object is given by:

Force = mass * acceleration
Force = (4.00 kg) * (9.8 m/s^2)
Force = 39.2 N

According to Hooke's law, this force is equal to the spring constant multiplied by the displacement of the spring:

39.2 N = k * (2.50 cm)

Solving for k, we get:

k = 39.2 N / (2.50 cm)
k = 15.68 N/cm

Now we can calculate the work done to stretch the spring 4.00 cm:

Work = (1/2) * (15.68 N/cm) * (4.00 cm)^2
Work = 125.44 N*cm

Therefore, the external agent must do 125.44 N*cm of work to stretch the same spring 4.00 cm from its unstretched position.

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