How Forces Affect Motion — CBSE Class 9 Science Important Questions

Answer: (b) remain at rest.

The forces are equal in size and opposite in direction, so they are balanced and the net force is zero. A zero net force cannot change the state of the box, so it stays at rest.

Answer: (b) Inertia.

Inertia is the natural tendency of an object to oppose a change in its state of motion; it is measured by the object's mass.

Answer: (a) $5\ \text{m s}^{-2}$5 m s^-2.

From $F=ma$F=ma, $a=\dfrac{F}{m}=\dfrac{10}{2}=5\ \text{m s}^{-2}$a=F/m=10/2=5 m s^-2.

Answer: (b) $3\ \text{m s}^{-2}$3 m s^-2.

Friction acts opposite to the push, so the unbalanced (net) force is $20-8=12\ \text{N}$20-8=12 N. Then $a=\dfrac{F_\text{net}}{m}=\dfrac{12}{4}=3\ \text{m s}^{-2}$a=F_net/m=12/4=3 m s^-2. Option (a) forgets friction.

Answer: (a) Both A and R are true and R is the correct explanation of A. Because of inertia of motion, the upper body continues to move forward when the bus stops, throwing the passengers forward.

Newton's second law: the acceleration of a body is directly proportional to the net (unbalanced) force acting on it and inversely proportional to its mass, and it is in the direction of the force. With SI units this gives $F=ma$F=ma.

One newton is the force that produces an acceleration of $1\ \text{m s}^{-2}$1 m s^-2 in a body of mass $1\ \text{kg}$1 kg: $1\ \text{N}=1\ \text{kg m s}^{-2}$1 N=1 kg m s^-2.

Acceleration $a=\dfrac{v-u}{t}=\dfrac{0-4}{2}=-2\ \text{m s}^{-2}$a=(v-u)/t=(0-4)/2=-2 m s^-2.

Force $F=ma=5\times(-2)=-10\ \text{N}$F=ma=5×(-2)=-10 N.

The force has magnitude $10\ \text{N}$10 N; the minus sign shows that it acts opposite to the motion (a retarding force).

The ball must be brought from high speed to rest. By drawing the hands back, the player makes the ball stop over a longer time.

For the same change in velocity, a longer time means a smaller deceleration, since $a=\dfrac{v-u}{t}$a=(v-u)/t. By the second law, $F=ma$F=ma, a smaller deceleration needs a smaller force, so the ball pushes on the hands with less force and the catch hurts less.

Balanced forces: forces acting on a body whose resultant is zero. They do not change the body's state of rest or of uniform motion; at most they change its shape. Example: in a tug of war where neither team moves, the two teams pull with equal and opposite forces.

Unbalanced forces: forces whose resultant is not zero. Example: when you push a stationary trolley harder than friction holds it back, it starts moving.

An unbalanced force can make a body at rest start moving, change its speed (speed it up or slow it down), or change its direction of motion. In each case it produces an acceleration.

Given $m=10\ \text{kg}$m=10 kg, $u=5\ \text{m s}^{-1}$u=5 m s^-1, $v=15\ \text{m s}^{-1}$v=15 m s^-1, $t=5\ \text{s}$t=5 s.

(i) $a=\dfrac{v-u}{t}=\dfrac{15-5}{5}=2\ \text{m s}^{-2}$a=(v-u)/t=(15-5)/5=2 m s^-2.

(ii) $F=ma=10\times2=20\ \text{N}$F=ma=10×2=20 N.

(a) First law: a body stays at rest, or keeps moving with uniform velocity in a straight line, unless an unbalanced force acts on it. It is called the law of inertia because it describes inertia, the natural tendency of a body to resist any change in its state of rest or motion.

(b) No. The ball stops because an unbalanced force acts on it: friction between the ball and the floor (and air resistance) acts opposite to its motion and slows it down. If there were no friction at all, the ball would keep rolling at the same speed, exactly as the first law says.

(c) Friction is useful when we walk: the grip between our feet and the ground stops us from slipping (brakes stopping a cycle is another example).

Friction can be reduced by (i) using lubricants such as oil or grease between moving parts, (ii) using ball bearings or wheels so that surfaces roll instead of slide, or (iii) making surfaces smooth or polished.

(a) Newton's third law: to every action there is an equal and opposite reaction, and the two act on different bodies. Example: when we walk, our foot pushes the ground backward (action) and the ground pushes us forward (reaction).

(b) Action: the person's feet push the boat backwards (force on the boat). Reaction: the boat pushes the person forwards (force on the person), towards the shore.

The two forces are equal in size and opposite in direction, but they act on different bodies, the person and the boat. Forces cancel only when they act on the same body, so each force produces its own effect: the person moves towards the shore and the boat moves away from it.

(i) Inertia (of motion). It is described by Newton's first law, the law of inertia.

(ii) $a=\dfrac{v-u}{t}=\dfrac{0-20}{0.5}=-40\ \text{m s}^{-2}$a=(v-u)/t=(0-20)/0.5=-40 m s^-2, so the deceleration is $40\ \text{m s}^{-2}$40 m s^-2.

(iii) With the air bag: $F=ma=60\times40=2400\ \text{N}$F=ma=60×40=2400 N. Without it: $a=\dfrac{20}{0.05}=400\ \text{m s}^{-2}$a=20/0.05=400 m s^-2, so $F=60\times400=24000\ \text{N}$F=60×400=24000 N.

(iv) The air bag makes the stopping time ten times longer, so the deceleration, and with it the force on the body ($F=ma$F=ma), is ten times smaller. A smaller force, spread over a larger area, causes far less injury.