The upper surface of a cube of gelatin, 5.5 cm on a side, is displaced 0.74 cm by a tangential force. If the shear modulus of the gelatin is 947 Pa, what is the magnitude of the tangential force?

To find the magnitude of the tangential force applied to the gelatin cube, we can use the formula for shear stress:

Shear Stress = Shear Modulus * Shear Strain

Where:
Shear Stress is the force per unit area acting tangentially to the surface,
Shear Modulus is a constant property of the material,
Shear Strain is the displacement per unit length of the material.

First, let's calculate the shear strain of the gelatin cube:

Shear Strain = Displacement / Original Length

Given that the displacement is 0.74 cm and the original length is 5.5 cm, we can substitute these values into the equation:

Shear Strain = 0.74 cm / 5.5 cm

Now, let's calculate the shear stress:

Shear Stress = Shear Modulus * Shear Strain

Given that the shear modulus is 947 Pa and the shear strain is the result from the equation above, we can substitute these values into the equation:

Shear Stress = 947 Pa * (0.74 cm / 5.5 cm)

Now, we have the shear stress, which is the force per unit area acting tangentially to the surface of the gelatin cube. To find the magnitude of the tangential force, we need to multiply the shear stress by the area of the surface.

The area of a cube is given by:

Surface Area = 6 * (Side Length)^2

Given that the side length of the cube is 5.5 cm, we can substitute this value into the equation:

Surface Area = 6 * (5.5 cm)^2

Now, we can calculate the magnitude of the tangential force by multiplying the shear stress by the surface area:

Magnitude of Tangential Force = Shear Stress * Surface Area

Substituting the values we have:

Magnitude of Tangential Force = (947 Pa * (0.74 cm / 5.5 cm)) * (6 * (5.5 cm)^2)

Calculating this expression will give us the magnitude of the tangential force applied to the gelatin cube.