Hooke's law — KCSE Physics

Hooke's Law states that the force exerted by a spring is directly proportional to its extension or compression. This can be expressed mathematically as:

F = kx
Where:

• F is the force applied (in Newtons),
• k is the spring constant (in N/m),
• x is the extension or compression of the spring (in meters).

To determine the spring constant, you can conduct an experiment using a spring and weights.

1. Hang a known weight from the spring and measure its extension.
2. Repeat with different weights to gather a range of data.
3. Plot a graph of force (F) against extension (x).
4. The slope of the line gives you the spring constant (k).

To construct a spring balance, follow these steps:

• Attach a calibrated scale to the spring.
• Ensure the spring is fixed at one end.
• Mark the scale in units of force based on the spring constant determined earlier.

This device can now measure the weight of objects by observing how much the spring stretches.

Hooke's Law states that the force (F) exerted by a spring is directly proportional to the extension (x) of the spring from its original length. This can be expressed mathematically as:

F = k * x

where:

• F is the force in newtons (N)
• k is the spring constant in newtons per meter (N/m)
• x is the extension in meters (m)

To solve numerical problems involving Hooke's Law, follow these steps:

1. Identify the values for force and extension.
2. Rearrange the formula if necessary to find the unknown.
3. Substitute the values into the equation and solve for the unknown.

For example, if a spring has a spring constant (k) of 200 N/m and is extended by 0.5 m, calculate the force exerted by the spring.

Solution:

• Given: k = 200 N/m, x = 0.5 m
• Using F = k * x,
• F = 200 N/m * 0.5 m = 100 N.

Thus, the force exerted by the spring is 100 N.

In physics, deformation refers to the change in shape or size of an object when a force is applied. Elastic deformation occurs when an object returns to its original shape after the force is removed. For example, a rubber band stretches but goes back to its initial form when released. Plastic deformation, on the other hand, is permanent; the object does not return to its original shape after the force is removed. An example of this is a clay model that retains its new shape after being shaped.

Elasticity is the property of a material that enables it to return to its original shape after deformation. The elastic limit is the maximum extent to which a solid can be deformed without undergoing permanent deformation. Beyond this limit, the material will experience plastic deformation.

In summary:

• Elastic deformation: Temporary change, returns to original shape.
• Plastic deformation: Permanent change, does not return.
• Elasticity: Ability to regain original shape.
• Elastic limit: Maximum deformation without permanent change.