Question

A 60-kg motor sits on four cylindrical rubber blocks. Each cylinder has a height of 3 cm and a cross-sectional area of 15 cm2. The shear modulus for this rubber is 2.0 MPa. A.) If a sideways force of 300 N is applied to the motor, how far will it move sideways? B.) With what frequency will the motor vibrate back and forth sideways if disturbed?

Answer 1

A.) If a sideways force of 300 N is applied to the motor, how far will it move sideways?

Answer 2

Part a)

`x = 3 mm`

Part b)

`f = 6.5 Hz`

Step-by-step explanation:

Part a)

As we know that shear modulus is given as

`\eta = (F/A)/(x/L)`

now we have

`x = (FL)/(\eta A)`

here we have

`F = 300 N`

`A = 15 cm^2`

`L = 3 cm`

`\eta = 2 * 10^6 Pa`

now we have

`x = (300 * 0.03)/((15 * 10^(-4))(2* 10^6))`

`x = 3 mm`

Part b)

As we know that

`F = (\eta A)/(L) x`

now the frequency of oscillation is given as

`f = (1)/(2\pi)\sqrt{(k)/(m)}`

here we know

`k = (\eta A)/(L)`

`k = (2* 10^6 * (15 * 10^(-4)))/(0.03)`

`k = 10^5`

`f = (1)/(2\pi)\sqrt{(10^5)/(60)}`

`f = 6.5 Hz`