Q: A force of 50 N is applied at an angle of $$60^\circ to a $$wrench that is 0.4 m long. What is the torque produced?

$$\tau = 0.4 \times 50 \times \sin(60^\circ) = 17.3\ \mathrm{Nm}$$

Q: A cylindrical steel rod (length $$L$$, diameter $$D) is $$subjected to a torque $$T. $$Which formula gives the angle of twist $$\theta if $$the shear modulus is $$G$$?

$$\theta = \dfrac{T \cdot L}{G \cdot J}$$, where $$J = \dfrac{\pi D^4$}{32}$$

Q: A 2 kg object is dropped from a height of 10 m. What is its potential energy just before it hits the ground? (Assume $$g = 9.81\ \mathrm{m/s^2$})$$

$$E_{pot} = 2 \times 9.81 \times 10 = 196.2\ \mathrm{J}$$

Q: A block is pushed 5 m along a surface by a force of 20 N at an angle of $$30^\circ to $$the direction of motion. How much work is done?

$$W = 20 \times \cos(30^\circ) \times 5 = 86.6\ \mathrm{J}$$

Question 1

Which of the following best describes the difference between accuracy and precision in measurements?

Accepted Answer

Accuracy is how close measurements are to the true value; precision is how reproducible the measurements are.

Question 2

A force of 50 N is applied at an angle of $$60^\circ to a $$wrench that is 0.4 m long. What is the torque produced?

Accepted Answer

$$	au = 0.4 	imes 50 	imes \sin(60^\circ) = 17.3\ \mathrm{Nm}$$

Question 3

A cylindrical steel rod (length $$L$$, diameter $$D) is $$subjected to a torque $$T. $$Which formula gives the angle of twist $$	heta if $$the shear modulus is $$G$$?

Accepted Answer

$$	heta = \dfrac{T \cdot L}{G \cdot J}$$, where $$J = \dfrac{\pi D^4$}{32}$$

Question 4

A 2 kg object is dropped from a height of 10 m. What is its potential energy just before it hits the ground? (Assume $$g = 9.81\ \mathrm{m/s^2$})$$

Accepted Answer

$$E_{pot} = 2 	imes 9.81 	imes 10 = 196.2\ \mathrm{J}$$

Question 5

Which of the following statements about the continuity equation for incompressible fluids is correct?

Accepted Answer

The product of area and velocity remains constant along the pipe: $$A_1$$ $$v_1$$ = $$A_2$$ $$v_2.$$

Question 6

A block is pushed 5 m along a surface by a force of 20 N at an angle of $$30^\circ to $$the direction of motion. How much work is done?

Accepted Answer

$$W = 20 	imes \cos(30^\circ) 	imes 5 = 86.6\ \mathrm{J}$$

Question 7

Which of the following is the correct formula for the buoyant force on a submerged object?

Accepted Answer

$$F_B = \rho_{fluid} \cdot g \cdot V_{submerged}$$

Question 8

A copper wire has a resistance $$R. If $$its length is doubled and its cross-sectional area is halved, what happens to its resistance?

Accepted Answer

Resistance increases by a factor of 4.

Question 9

Which of the following best describes the function of a diode in an electronic circuit?

Accepted Answer

It allows current to flow in only one direction.

Question 10

A 10 $$\Omega$$ and a 20 $$\Omega$$ resistor are connected in parallel. What is the total resistance?

Accepted Answer

$$R_{total} = \dfrac{1}{\dfrac{1}{10} + \dfrac{1}{20}} = 6.67\ \Omega$$

Question 11

Which of the following is the correct expression for stress in a material?

Accepted Answer

$$\sigma = \dfrac{F}{A}$$

Question 12

A balloon at 25$$^\circC (298 K) $$and 1 atm is heated to 60$$^\circC (333 K) at $$constant pressure. If the initial volume is $$V_1$$, what is the new volume $$V_2$$?

Accepted Answer

$$V_2$$ = $$V_1$$ 	imes \dfrac{333}{298}$$

Question 13

Which of the following is NOT an assumption for Bernoulli’s equation to be valid?

Accepted Answer

The fluid is compressible.

Question 14

A spring with $$k = 200\ \mathrm{N/m} is $$stretched by $$0.05\ \mathrm{m}. $$What is the force required?

Accepted Answer

$$F = 200 	imes 0.05 = 10\ \mathrm{N}$$

Question 15

Which of the following best explains why ships float?

Accepted Answer

The average density of the ship (including air inside) is less than the density of water.

Question 16

Which of the following is the correct formula for the period $$T of a $$wave with frequency $$f$$?

Accepted Answer

$$T = \dfrac{1}{f}$$

Question 17

A 5 kg object moving at 4 m/s collides and sticks to a 3 kg object at rest. What is their final velocity?

Accepted Answer

$$v_f = \dfrac{5 	imes 4}{5 + 3} = 2.5\ \mathrm{m/s}$$

Question 18

Which of the following is the correct formula for the energy stored in a stretched spring?

Accepted Answer

$$E_{spring} = \dfrac{1}{2} k x^2$

Fluid Mechanics, Forces, and Material Properties: Essential Physics Concepts

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