How Forces Affect Motion

The paddle pushes water backward. The water pushes the paddle and canoe forward with an equal and opposite force (Newton’s third law). A harder push gives a larger forward force, so the canoe accelerates more, if other conditions stay the same.

The empty canoe has less mass. For the same net force, a smaller mass gets greater acceleration (a = F/m).

Earth pulls the barbell downward (weight), and the lifter pushes it upward. If it is steady, these forces are equal and opposite, so the net force is zero.

Unbalanced forces; S pushes harder towards the front.

The stretched band gives the stack a push. After it leaves the band, friction slows it down. It usually travels farther on smoother surfaces, where friction is smaller, and a shorter distance on rougher surfaces. Repeat trials and compare average distances.

As the pull increases, static friction matches it until the block is about to move. At that point the spring-balance reading estimates the maximum static friction. Compare readings across surfaces; rougher contact often gives a larger reading.

After a push sets it moving, it would continue in a straight line at constant velocity. With no friction or other net force, nothing would slow it down (Newton’s first law).

Keep the cart mass fixed and increase the hanging mass to increase the pulling force. If the cart covers the same distance in less time, its acceleration is greater. The results show that, for fixed mass, acceleration increases with net force.

The heavier cart accelerates less. For a fixed net force, acceleration is inversely proportional to mass: a = F/m.

No. The forces balance, so net force is zero. Since the box is already moving, it continues with the same constant velocity (in the ideal model).

(i) and (ii) are possible. (iii) is not: zero net force means zero acceleration.

A book resting on a table has gravity pulling down and the table’s normal force pushing up with equal strength. Forces act, but they balance, so the book does not accelerate.

(a) Same direction: 10 + 6 = 16 N right. (b) Opposite: 10 − 6 = 4 N right. (c) Opposite: 10 − 6 = 4 N left, because the 6 N force is larger in that direction.

Total mass = 10 + 10 + 10 = 30 kg. Weight = mg = 30 × 9.8 = 294 N downward. To keep it steady, the lifter applies 294 N upward.

Push and friction are equal and opposite, so net force is zero. Since the block starts at rest, it stays at rest. Displacement = 0 m.

Net force = 55 − 50 = 5 N. Acceleration a = F/m = 5/25 = 0.2 m s⁻². From rest, s = ½at² = 0.5 × 0.2 × 2² = 0.4 m forward.

F = ma: (i) 3000 N east; (ii) 0 N; (iii) 3000 N west.

The balloon pushes air backward as it escapes. The air pushes the balloon forward with an equal and opposite force. This is Newton’s third law.

Use a = F/m. Bullet: 2/0.1 = 20 m s⁻². Gun: 2/5 = 0.4 m s⁻². Their accelerations are opposite; the lighter bullet accelerates more.

The same force causes acceleration a = F/m. Earth’s mass is enormous, so its acceleration is far too small to notice; the fruit’s much smaller mass gives a noticeable acceleration.

Constant velocity means zero acceleration and zero net force. Friction has magnitude F and acts opposite the motion.

(i) Velocity stays the same. (ii) Speed increases. (iii) Speed decreases. A net force changes velocity in its own direction.

P has a net force of 1 N toward the 5 N force. Q has zero net force because constant velocity means no acceleration. Correct choice: (i).

Forward force = 95 × 200 = 19,000 N. Backward force = 5 × 200 = 1,000 N. Net force = 19,000 − 1,000 = 18,000 N forward.

Acceleration is in the direction of the net force and is directly proportional to the net force for a fixed mass. Correct choice: (iv).

Only C. Its position-time graph is curved, so its velocity changes and a net force acts.

Yes. The sailor pushes the boat backward while jumping forward. The boat recoils backward due to the equal and opposite interaction force.

The soft mat increases the time over which the athlete stops. For the same change in momentum, a longer stopping time means a smaller force, reducing injury risk.

Neither. They exert equal magnitude forces on each other in opposite directions (Newton’s third law). Their accelerations may differ because their masses differ. Correct choice: (iv).

F = ma = 1 × 10 = 10 N. Draw a horizontal line at 10 N.

a = (30 − 10)/8 = 2.5 m s⁻²; F = 10 × 2.5 = 25 N.

v² = u² + 2as: a = −10,000 m s⁻²; F = ma = −500 N. Magnitude: 500 N, opposite motion.

108 km h⁻¹ = 30 m s⁻¹; t = mv/F = (0.4 × 30)/800 = 0.015 s.

Fnet = −(7 + 3) = −10 N; a = −5 m s⁻²; v² = u² + 2as gives s = 10 m.

From F = m₁a₁, m₁ = F/a₁. Similarly m₂ = F/a₂. Together: a = F/(m₁ + m₂) = F/[F/a₁ + F/a₂] = a₁a₂/(a₁ + a₂).

The forces are equal and opposite but act on different objects. The compass has much less mass and so gets a larger acceleration. The magnet also accelerates, but its much greater mass and friction/support make its motion too small to notice.

Use the same block and surface. Pull it with a spring balance, first recording the largest force just before it moves, then the steady force while sliding. Add known masses to increase how hard surfaces press together and repeat. Keep the surface and pulling speed controlled; record repeated readings and compare.

Place equal-mass cars together with like poles facing and release them on a level smooth track. Measure their distances and times in opposite directions. Repeat with equal added masses on both cars. Compare results; ideally forces are equal and opposite, while real distances also depend on friction, alignment, and magnets.

Each extra turn increases contact and friction between rope and post. The post then provides a stronger grip, so less hand force is needed to keep the bucket from slipping.