Principles of Motion and Forces Flashcards

A 1,200 kg vehicle accelerates from 10 m/s to 30 m/s over a period of 5 seconds. What is the average net force acting on the vehicle during this acceleration?

Answer: 4,800 N

First, calculate the acceleration (a) using the formula a = (vf - vi) / t, where vf is the final velocity, vi is the initial velocity, and t is time. So, a = (30 m/s - 10 m/s) / 5 s = 4 m/s². Next, use Newton's Second Law of Motion, F = ma, where F is force, m is mass, and a is acceleration. F = 1,200 kg * 4 m/s² = 4,800 N.

Which of the following scenarios best illustrates Newton's First Law of Motion (the law of inertia)?

Answer: A book remains on a table until a person picks it up.

Newton's First Law of Motion states that an object at rest will stay at rest, and an object in motion will stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force. A book remaining at rest on a table is a direct example of this principle, as it will not move without an external force.

A sailor uses a pulley system to lift a 50 kg crate of supplies 4 meters vertically from the dock to the ship's deck. How much work is done on the crate against gravity? (Assume g ≈ 10 m/s²)

Answer: 2000 J

Work done against gravity is calculated as W = mgh, where m is mass, g is the acceleration due to gravity, and h is the vertical height. The force required to lift the crate is equal to its weight (mg). W = (50 kg) * (10 m/s²) * (4 m) = 2000 Joules.

A projectile is fired from a naval gun with an initial velocity. Neglecting air resistance, which of the following statements is true about its motion?

Answer: Its horizontal velocity is constant.

In projectile motion (without air resistance), the only force acting on the object after it is fired is gravity, which acts vertically. This means there is no horizontal acceleration, so the horizontal component of the velocity remains constant throughout the flight. The vertical velocity changes due to gravity, and the net force is never zero while it's in the air.

Two sailors on frictionless ice skates are at rest. Sailor A (80 kg) pushes Sailor B (100 kg), causing Sailor B to move away at a speed of 2 m/s. What is the recoil speed of Sailor A?

Answer: 2.5 m/s

This scenario is governed by the principle of conservation of momentum. The total momentum before the push is zero. Therefore, the total momentum after the push must also be zero. The momentum of Sailor B is pB = mB * vB = 100 kg * 2 m/s = 200 kg·m/s. To conserve momentum, Sailor A must have an equal and opposite momentum: pA = -200 kg·m/s. The speed of Sailor A is vA = pA / mA = -200 kg·m/s / 80 kg = -2.5 m/s. The speed is the magnitude, which is 2.5 m/s.

A constant force is applied to an object, causing it to accelerate. If the force is doubled and the object's mass is halved, what is the effect on the object's acceleration?

Answer: It is quadrupled.

According to Newton's Second Law, acceleration (a) is directly proportional to the net force (F) and inversely proportional to the mass (m), as shown in the formula a = F/m. Let the initial acceleration be a1 = F/m. The new force is F2 = 2F, and the new mass is m2 = m/2. The new acceleration is a2 = F2/m2 = (2F) / (m/2) = 4 * (F/m) = 4 * a1. Therefore, the acceleration is quadrupled.