Mechanical Comprehension Practice Test 4

Correct answer: C — 91 joules

Work is calculated using the formula Work = Force × Distance. Therefore, Work = $$65\text{ N} \times 1.4\text{ m} = 91$$ joules.

Correct answer: B — 375 kilograms

A five-pulley setup provides a mechanical advantage (MA) of 5. Multiplying the base effort load by 5 gives the maximum liftable load: $$75\text{ kg} \times 5 = 375$$ kilograms.

Correct answer: A — 30

Mechanical Advantage (MA) is calculated as Load Force / Effort Force. Thus, MA = $$\frac{8{,}100\text{ N}}{270\text{ N}} = 30$$

Correct answer: A — 5 feet

Using the work principle for an inclined plane (Effort Force × Ramp Length = Weight × Vertical Height): 100 lb × 20 ft = 400 lb × Height. Thus, $$2{,}000 = 400 \times \text{Height}$$, giving Height = 5 feet.

Correct answer: B — 3,200 newtons

The actual mechanical advantage (AMA) represents the performance:

AMA = Ideal mechanical advantage × Performance = $$16 \times 0.80 = 12.8$$.

The maximum weight (load) that can be lifted is Load = Applied force × AMA $$= 250\text{ N} \times 12.8 = 3{,}200$$ Newtons.

Correct answer: B — Kinetic energy

According to the law of conservation of energy, the elastic potential energy stored in the bent bow string converts directly into mechanical kinetic energy as the arrow gains velocity and motion.

Correct answer: A — It will float on top of the freshwater layer.

An object floats on any liquid that is denser than itself. Since the plastic block's density (0.88 g/cm³) is less than that of freshwater (1.00 g/cm³), it will float on top of the freshwater layer without sinking into it.

Correct answer: C — Sphere A reaches the bottom first, but both spheres arrive with the same final speed.

Sphere A has a steeper slope, giving it a greater component of gravitational acceleration $$(a = g \sin\theta)$$ and allowing it to reach the bottom in less time. However, by conservation of energy ($$mgh = \frac{1}{2} m v^2$$), both spheres convert the exact same initial potential energy into kinetic energy, resulting in identical final speeds ($$v = \sqrt{2gh}$$) at the bottom.

Correct answer: D — 300 N

Torque is defined as Torque = Force × Distance (lever arm). The first wrench produces a torque of $$\tau = 150\text{ N} \times 0.30\text{ m} = 45\text{ N}\cdot\text{m}$$. To match this torque with half the handle length (0.15 m), the required force is Force $$= \frac{45\text{ N}\cdot\text{m}}{0.15\text{ m}} = 300\text{ N}$$

Correct answer: B — 50 kg

Useful Power Output = Total Power × Efficiency = $$700\text{ W} \times 0.70 = 490\text{ W}$$.

Total Useful Work performed = Useful Power × Time $$= 490\text{ W} \times 10\text{ s} = 4{,}900$$ Joules.

Since Work $$= m \times g \times h$$, we have $$4{,}900\text{ J} = m \times 9.8\text{ m/s}^2 \times 10\text{ m} = 98m$$. Solving for mass gives $$m = \frac{4{,}900}{98} = 50$$ kg.

Correct answer: A — 124 pounds

Using rotational equilibrium (Sum of Torques = 0) about the right scale (pivot at $$x = 10$$ ft):

$$F_{\text{left}} \times 10\text{ ft} = (30\text{ lb} \times 6\text{ ft}) + (120\text{ lb} \times 8\text{ ft}) + (50\text{ lb} \times 2\text{ ft})$$

$$F_{\text{left}} \times 10 = 180 + 960 + 100 = 1240$$ lb·ft

$$F_{\text{left}} = \frac{1240}{10} = 124$$ pounds.

(Note: 76 pounds is the reading on the right scale).