NCERT Exemplar Class 11 Physics Solutions Chapter 5 Laws of Motion

NCERT Exemplar Class 11 Physics Solutions Chapter 5 MCQI

Question:5.1

A ball is travelling with uniform translatory motion. This means that
(a) it is at rest.
(b) the path can be a straight line or circular and the ball travels with uniform speed.
(c) all parts of the ball have the same velocity (magnitude and direction) and the velocity is constant.
(d) the centre of the ball moves with constant velocity and the ball spins about its centre uniformly.

Answer:

The answer is the option (c) All particles of the ball have the same velocity (magnitude and direction), and the velocity is constant.
Explanation: Uniform motion or uniform translatory motion is the one in which all the particles of a body move in a straight line and with the same velocity.

Question:5.2

A metre scale is moving with uniform velocity. This implies
(a) the force acting on the scale is zero, but a torque about the centre of mass can act on the scale.
(b) the force acting on the scale is zero and the torque acting about centre of mass of the scale is also zero.
(c) the total force acting on it need not be zero but the torque on it is zero.
(d) neither the force nor the torque need to be zero.

Answer:

The answer is the option (b) The net force acting on the scale is zero, and the net torque acting about the centre of mass of the scale is also zero.
Explanation: There is no change in velocity as the meter scale is moving with uniform velocity
Therefore, by Newton’s second law, its acceleration will be zero.

Hence, the net or resultant force acting on the body must be 0.
Now,
Therefore, toque must be zero as well.
Hence it is obvious that for an object to move with uniform velocity, both net force and torque must be zero.

Question:5.3

A cricket ball of mass 150 g has an initial velocity
and a final velocity after being hit. The change
in momentum (final momentum-initial momentum) is (in kg m s¹ )
(a) zero
(b)
(c)
(d)

Answer:

The answer is the option (c)
Explanation: Here, m = 150g = 0.15 kg
&

Now, we know that
Change in momentum = Final momentum – initial momentum




Therefore,

Question:5.4

In the previous problem (5.3), the magnitude of the momentum transferred during the hit is
(a) Zero
(b) 0.75
(c) 1.5
(d) 14

Answer:

The answer is the option (c) 1.5
Explanation: Change in momentum = Final momentum – initial momentum
Thus, its magnitude will be,

Question:5.5

Conservation of momentum in a collision between particles can be understood from
(a) conservation of energy.
(b) Newton’s first law only.
(c) Newton’s second law only.
(d) both Newton’s second and third law.

Answer:

. The answer is the option (d) Both Newton’s second and third law
Explanation: (ii) ……. (By Newton’s second law)

By the law of conservation of momentum

Thus, hence, = constant

(ii) Newton’s third law states that every action has an equal, opposite and instantaneous reaction, i.e., action force is equal to reaction force in magnitude but opposite in direction.



Hence, option (d).

Question:5.6

A hockey player is moving northward and suddenly turns westward with the same speed to avoid an opponent. The force that acts on the player is
(a) frictional force along westward.
(b) muscle force along southward.
(c) frictional force along south-west.
(d) muscle force along south-west.

Answer:

The answer is the option (c) friction force along the south-west.
Explanation: The force on the player is a result of the rate of change of momentum. The direction of change in momentum, i.e., is the same as the direction of force acting on the player and is towards the south-west, viz., the direction of the force on the player.

Question:5.7

A body of mass 2kg travels according to the law where and . The force acting on the body at t = 2 seconds is
(a) 136 N
(b) 134 N
(c) 158 N
(d) 68 N

Answer:

The answer is the option (a) 136N
Explanation:



thus,


Now, we know that,

Thus,

Question:5.8

A body of mass 5kg is acted upon by a force . If its intial velocity at t=0 is , the time at which it will just have velocity along the y-axis is
(a) never
(b) 10 s
(c) 2 s
(d) 15 s

Answer:

The answer is the option (b) 10s
Explanation:
Initial velocity
Force, , Mass (m) = 5kg

Since there is only Y component in final velocity and the X component is zero,

t = 10s.

Question:5.9

A car of mass m starts from rest and acquires a velocity along east in two seconds. Assuming the car moves with uniform acceleration, the force exerted on the car is
a) eastward and is exerted by the car engine
b) eastward and is due to the friction on the tyres exerted by the road
c) more than eastward exerted due to the engine and overcomes the friction of the road
d) exerted by the engine

Answer:

The answer is the option (b) eastward and is due to friction on tyres exerted by the road.
Explanation: Here,
We know that, v = u + at



The force by the engine is an internal force.

NCERT Exemplar Class 11 Physics Solutions Chapter 5 MCQII

Question:5.10

The motion of a particle of mass m is given by x = 0 for t < 0 s, x( t ) = A sin 4p t for 0 < t <(1/4) s (A > o), and x = 0 for t >(1/4) s. Which of the following statements is true?
(a) The force at t = (1/8) s on the particle is
(b) The particle is acted upon by on impulse of magnitude at t = 0 s and t = (1/4) s.
(c) The particle is not acted upon by any force.
(d) The particle is not acted upon by a constant force.
(e) There is no impulse acting on the particle.

Answer:

The correct answer is: -
(a) The force at s on the particle is
(b) The particle is acted upon by on impulse of magnitude at t = 0s and
(d) The particle is not acted upon by a constant force.
Explanation: Here, mass = m
Thus, x(t) = 0, for t<0

and

Now,
For




Now, it’s clear that force is a function of time, hence opt (d) is verified.
(a) At


thus, force at

Hence,
Hence, opt (a)
(b) Impulse = Change in momentum between the values t = 0s and
Now we already know from above that, F(t) varies from 0 at t = 0s to the max. value at at & by the eq. at .

Hence opt (b).

Question:5.11

In Figure, the co-efficient of friction between the floor and the body B is 0.1. The co-efficient of friction between the bodies B and A is 0.2. A force F is applied as shown on B. The mass of A is and of B is m. Which of the following statements are true?

(a) The bodies will move together if F = 0.25 mg.
(b) The body A will slip with respect to B if F = 0.5 mg.
(c) The bodies will move together if F = 0.5 mg.
(d) The bodies will be at rest if F = 0.1 mg.
(e) The maximum value of F for which the two bodies will move together is 0.45 mg.

Answer:

The correct answer is: -
(a) The bodies will move together at if.
(b) The body A will slip with respect to B if .
(d)The bodies will be at rest if .
(e) The maximum value of for which the two bodies will move together is 0.45 mg.
Explanation: By opt (e) the max. force by which bodies move together is 0.45 mg Newton.
mA = = mB = m
Consider the acceleration of the bodies A and B to be ‘a’.
Both the bodies A & B will keep moving by force F until the force of friction between their surface is larger or equal to 0 than the force acting on A.



Thus, the force on

Hence, the force on A is

The body A will move along with body B only if F_AB is equal or smaller than f₂.
Hence,

……… (i)

N is the reaction force by B on A
……… (here, N_B is the normal reactn on B along with A by the surface)

………… (ii)
Now,
……….. [from (i)]

…………. (iii)
Thus, the max force on B is 0.45mg, therefore, A & B can move together.
Hence, opt (e).
Both the bodies A & B will keep moving by force F until the force of friction between their surface is larger or equal to 0 than the force acting on A, i.e., 0.45 mg Newton, hereby opt (c) is rejected.
Now, for opt (d), the minimum force which can move A & B together is,

….. [from (i) & (ii)]
Newton
Since 0.1mg<0.25 mg, opt (d) is verified which states that the body will be at rest if

Question:5.12

Mass moves on a slope making an angle with the horizontal and is attached to mass by a string passing over a frictionless pulley as shown in Figure. The co-efficient of friction between and the sloping surface is .

Which of the following statements are true?
(a) If , the body will move up the plane.
(b) If , the body will move up the plane.
(c) If , the body will move up the plane.
(d) If , the body will move down the plane.

Answer:

The correct answer is: -
(b) If , the body will move up the plane.
(d) If , the body will move down the plane.
Explanation:

Case I-
Considering the first case, normal reaction (N) =
Now, , which becomes,


m₁ will be up, and m₂ will be down when


or
hereby, opt (b) is verified and opt (a) is rejected.
Case II-
Now, considering that if the body m1 moves down and the body m2 up then, direct of f becomes upward (i.e., opposite to the motion).




Hence, option (d) is verified here, as well as opt (c) is rejected.

Question:5.13

In Figure, a body A of mass m slides on plane inclined at angle to the horizontal and is the coefficient of friction between A and the plane. A is connected by a light string passing over a frictionless pulley to another body B, also of mass m, sliding on a frictionless plane inclined at angle to the horizontal. Which of the following statements are true?

(a) A will never move up the plane.
(b) A will just start moving up the plane when
(c) For A to move up the plane, must always be greater than .
(d) B will always slide down with constant speed.

Answer:

The correct answer is the option:
(b) A will just start moving up the plane when
(c) For A to move up the plane, must always be greater than .
Explanation:

In the fig. below,= coefficient of friction of A whereas B is on a frictionless surface.
(i) when A is about to start


When A just start moving upward


If on the plane, the body A moves upward, and B moves downward



Hence, opt (c) is verified and opt (a) is rejected.

(ii) If the body B moves upward and A moves downward then,



Since and are acute angles, > , thus, may be true
Since it is now clear that body B can also move upward, opt (d) is also rejected.

Question:5.14

Two billiard balls A and B, each of mass 50g and moving in opposite directions with speed of 5m s-1 each, collide and rebound with the same speed. If the collision lasts for , which of the following statements are true?
(a) The impulse imparted to each ball is 0.25 kg m s^-1 and the force on each ball is 250 N.
(b) The impulse imparted to each ball is 0.25 kg m s^-1 and the force exerted on each ball is 25 × 10^-5 N.
(c) The impulse imparted to each ball is 0.5 Ns.
(d) The impulse and the force on each ball are equal in magnitude and opposite in direction.

Answer:

The correct answer is:
(c) The impulse imparted to each ball is 0.5 Ns.
(d) The impulse and force on each ball are equal in magnitude and opposite in direction.
Let m be the mass of each ball, m = 0.05 kg
Let v be the speed of each ball, v = 5m/s
We know that the initial momentum of each ball will be


= 0.25 N-s ……….. (i)
After the collision, on rebounding, the direction of the velocity of each ball is reversed; hence, the final momentum of each ball will be

=- 0.25 N-s.
Hence, opt (d) is verified.
Thus, it is clear that impulse imparted to each ball is equal to change in momentum of each ball

= - 0.25 – (0.25)
= -0.50 kg ms^-1
= -0.50 N-s
Here opt (c) is also verified.

Question:5.15

A body of mass 10 kg is acted upon by two perpendicular forces, 6N and 8N. The resultant acceleration of the body is
(a) 1 m at an angle of w.r.t. 6N force.
(b) 0.2 m at an angle of w.r.t. 6N force.
(c) 1 m at an angle of w.r.t. 8N force.
(d) 0.2 m at an angle of w.r.t. 8N force.

Answer:

The correct answer is:
(a) 1 m at an angle of w.r.t. 6N force.
(c) 1 m at an angle of w.r.t. 8N force.
Explanation:
Here we know that,

m = 10kg, F₂ = 8N & F₁ = 6N



Thus, R = 10 N
………. (i)
………… (ii)
……….. (iii)
Hence, opt (a) is verified from (i) and (ii), whereas opt (c) is verified from (i) and (iii).
Since, acceleration is not equal to 0.2 ms^-2, opt (b) & (d) are rejected.

NCERT Exemplar Class 11 Physics Solutions Chapter 5 Very Short Answer

Question:5.16

A girl riding a bicycle along a straight road with a speed of 5 m s^-1 throws a stone of mass 0.5 kg which has a speed of 15 m s^-1 with respect to the ground along her direction of motion. The mass of the girl and bicycle is 50 kg. Does the speed of the bicycle change after the stone is thrown? What is the change in speed, if so?

Answer:

Here it is given that: m₁ = 50kg & m₂ = 0.5 kg
u₁ = 5 m/s forward & u₂ = 5 m/s forward
v₂ = 15 m/s forward
To find: v₁ = ?
By the law of conservation of momentum-
Initial momentum (i.e., girl, cycle & body) = Final momentum (girl, cycle & body)



Thus,
Thus, the speed of the cycle and the girl is reduced by 5 – 4.9 = 0.1 m/s.

Question:5.17

A person of mass 50 kg stands on a weighing scale on a lift. If the lift is descending with a downward acceleration of 9 m s^-2, what would be the reading of the weighing scale? (g = 10 ms² )

Answer:

The apparent weight would decrease on the weighing scale if the lift is descending with an acceleration ‘a’.
Thus, W’ = R = (mg – ma)
= m (g – a)
Due to reaction force, apparent weight by the lift on the weighing scale would be,
W’ = 50 (10 – 9) =50 N
Thus, the reading of the weighing scale would be

Question:5.18

The position time graph of a body of mass 2 kg is as given in Figure. What is the impulse on the body at t = 0 s and t = 4 s.

Answer:

m = 2kg
Let v1 be the initial velocity, v₁ = 0, from the graph t ≥ 0 to t ≤ 4, viz., a straight line. Hence, the velocity of the body will be constant.

At t ≥ 4,
The slope of the graph is zero; hence, the velocity v₃ = 0.
Now, impulse =
We know that impulse is the change in momentum,
Impulse at t = 0;
= 2[0.75 – 0]
= 1.50 kg ms^-1
Impulse at t = 4;
=
=2 [0 – 0.75]
=-1.50 kg ms^-1
Therefore, at t = 0, impulse increases by +1.5kg ms^-1 &
At t = 4, impulse decreases by 1.5 kg ms^-1

Question:5.19

A person driving a car suddenly applies the brakes on seeing a child on the road ahead. If he is not wearing seat belt, he falls forward and hits his head against the steering wheel. Why?

Answer:

Due to inertia of motion, if a person applies breaks suddenly, then that person’s lower part slows down rapidly, but the upper part continues to move in the same direction and with the same speed & thus he/she ends up hitting his/her head against the steering wheel of the car.

Question:5.2

The velocity of body mass 2kg as a function of t is given by Find the momentum and the force acting on it, at t=2 s.

Answer:

Given data: m = 2kg

At t = 2s,

Now, momentum








Thus,

Question:5.21

A block placed on a rough horizontal surface is pulled by a horizontal force F. Let f be the force applied by the rough surface on the block. Plot a graph of f versus F.

Answer:

Here,
A is the limiting frictional force & at B = kinetic frictional force.

Question:5.22

Why are porcelain objects wrapped in paper or straw before packing for transportation?

Answer:

During transportation, sudden jerks or falls takes place.
Porcelain objects are brittle and can break due to small jerks and falls, that’s why they are packed in paper or straw which provides them with more time to stop or change velocity during jerks and hence decreasing the acceleration. Hence the objects become safer since the force on them will be smaller.

Question:5.23

Why does a child feel more pain when she falls down on a hard cement floor, than when she falls on the soft muddy ground in the garden?

Answer:

From the formula ‘F = ma’, we can tell that if mass is kept constant then acceleration ‘a’ should be decreased for a system to decrease force.
Now, , for a falling body, initial velocity will be u and final velocity will be 0. The acceleration and force will decrease, if the time during hitting is increased. Pain acts on a person when he/she falls on a cemented hard floor as the time to stop after fall is very small, whereas, after falling on a soft floor he/she sinks in the ground and takes more time to stop.

Question:5.24

A woman throws an object of mass 500 g with a speed of 25 m s¹.
(a) What is the impulse imparted to the object?
(b) If the object hits a wall and rebounds with half the original speed, what is the change in momentum of the
object?

Answer:

(a) Given: m = 500g
= 0.5 kg,
u =0 & v = 25 m/s.
We know that,


= 0.5 (25 – 0)
= 12.5 N-s
(b) Here, m = 0.5 kg
u = +25 ms^-1 (forward)
v = ms^-1 (as backward)
Thus,

= 0.5 [ -12.5 – 25]

Therefore,
Therefore, or or the force is opposite to the initial velocity of the ball.

Question:5.25

Why are mountain roads generally made winding upwards rather than going straight up?

Answer:

When talking about inclined planes, for a body going upwards, the force of friction is , where is the angle of inclination of a plane.
The force of friction is high if is small, and hence there is less chance of skidding.
The value of friction will be smaller for a road straight up the mountain since it will have a larger angle of inclination, and thus the chance of skidding will be more.

NCERT Exemplar Class 11 Physics Solutions Chapter 5 Short Answer

Question:5.26

A mass of 2 kg is suspended with thread AB (Figure). Thread CD of the same type is attached to the other end of 2 kg mass. Lower thread is pulled gradually, harder and harder in the downward direction so as to apply force on AB. Which of the threads will break and why?

Answer:

The force on CD = force applied at D downward,
whereas the Force on AB = Force F along with force due to mass 2 kg downward.
Thus, the force on AB is more than fore at D by 2 kg, which will lead to the breakup of thread AB.
Hence, thread AB will break.

Question:5.27

In the above given problem if the lower thread is pulled with a jerk, what happens?

Answer:

If the thread CD is pulled with a jerk it will break since due to inertia of rest, pull on thread CD is not transmitted to thread AB by 2 kg mass.

Question:5.28

Two masses of 5 kg and 3 kg are suspended with help of massless inextensible strings as shown in the figure. Calculate and when whole system is going upwards with acceleration = 2 m/s².

Answer:

We know that the whole system is going up with acceleration,
In all parts of the string, tension is equal and opposite.
The forces acting on mass m₁ –





The forces acting on mass m₂ –


=3 (9.8 + 2)
=3(11.8)
= 35.4
Now,
= 35.4 + 59
Thus,

Question:5.29

Block A of weight 100 N rests on a frictionless inclined plane of slope angle (Figure). A flexible cord attached to A passes over a frictionless pulley and is connected to block B of weight W. Find the weight W for which the system is in equilibrium.

Answer:

In this problem, the main concept used is of ‘on balance condition’, viz., if there is no motion, then there will be no frictional force or f=0.
During the equilibrium of A or B, mg sin
…… (since mg is 100N)
Thus,
= 50
Hence, when B is at rest,
W = F = 50N.

Question:5.30

A bock of mass M is held against a rough vertical wall by pressing it with a finger. If the coefficient of friction between the block and the wall is and the acceleration due to gravity is g, calculate the minimum force required to be applied by the ginger to hold the block against the wall?

Answer:

Let M be the mass of the body which is held against the wall by force F. When the condition is balanced, F = N

The minimum force required to hold the block against the wall at rest is

Question:5.31

A 100 kg gun fires a ball of 1 kg horizontally from a cliff of height 500 m. It falls on the ground at a distance of 400 m from the bottom of the cliff. Find the recoil velocity of the gun.

Answer:

Let u ms^-1 be the horizontal speed of the ball & its vertical component will be zero. If we consider the motion od the ball vertically downward then,
u = 0, s = h = 500m
g = 10sm^-2,

We know that,

= 10 s
Its horizontal range will be equal to

Thus, v = 40 m/s
is the mass of the ball
is the mass of the gun
is the initial velocity of the ball
is the final velocity of the gun
& is the final velocity of the ball
Thus
Therefore, the recoil velocity of the gun will be , viz., opposite to the speed of the ball.

Question:5.32

Figure shows (x, t), (y, t ) diagram of a particle moving in 2-dimensions.


If the particle has a mass of 500g find the force (direction and magnitude) acting on the particle.

Answer:

By graph (a),
= 1 ms^-1

By graph (b),
Thus,

Thus,
m = 500g = 0.5 kg

= 1 N, towards Y-axis

= 0 N

Hence, F = 1 N, towards the Y-axis.

Question:5.33

A person in an elevator accelerating upwards with an acceleration of 2 m/s², tosses a coin vertically upwards with a speed of 20 m/s. After how much time will the coin fall back into his hand?

Answer:

Let ‘a’ be the upward acceleration of the elevator, a = 2m/s²
g = 10 ms^-2
Thus the net effective acceleration, viz., a’ is equal to (a+g)
Thus a’ = (2+10)
a’ = 12 ms^-1
Now, considering the effective motion of the coin, v = 0 & t = time taken by the coin to achieve maximum height
u = 20 ms^-1 and a’ = 12 ms^-2
thus, v=u + at here a = a’
0 = 20 – 12t
Therefore,
Thus, time of ascend = time of descend
Therefore, after achieving maximum height, total time to return in hand will be equal to

=
= seconds.

NCERT Exemplar Class 11 Physics Solutions Chapter 5 Long Answer

Question:5.34

There are three forces , and acting on a body, all acting on a point P on the body. The body is found to move with uniform speed.
a) show that the forces are coplanar
b) show that the torque acting on the body about any point due to these three forces is zero

Answer:

(a) The acceleration of the body is zero since it is moving with uniform speed due to the action of the forces , and on a point on the body. It has no circular motion.
Since, F = ma, resultant force will be


Let us consider that the forces as well as the resultant of these forces, are in the same plane of the paper, but in it is in the same plane except for the direction which is rephrased.
will be in the same plane since , hence are coplanar.
(b) The resultant of is zero, therefore, its torque=

Hence, the torque acting on the body at any point will be zero.

Question:5.35

When a body slides down from rest along a smooth inclined plane making an angle of with the horizontal, it takes time T. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it is seen to take time pT, where p is some number greater than 1. Calculate the coefficient of friction between the body and the rough plane.

Answer:

Since the body slides down from rest along a smooth plane viz. inclined at in time ‘T’.
u=0, s=s & t=T,




Now,

The motion of the body along a rough plane,
u=0,

………… (i)


=



Now,
…….. (ii)


It is given that in both cases the distance is equal

Question:5.36

Below figures show and diagrams for a body of unit mass. Find the force as a function of time.

Answer:

From fig. (a),
V_x = 2t, for 0 < t < 1s
a_x = 2/1 = 2, for 0 < t < 1s
, for 1 < t < 2s
a_x= -2, for 1 < t < 2s
thus, F_x= ma (m = 1…..given)
= 1(2) =2, for 0 < t < 1s
& F_x = 1(-2)
= -2, for1 < t < 2s
From fig. (b),

=1 ms^-1, for 0 < t < 1
F_y = ma
= 1.1 = 1 unit, for 0 < t < 1
a_y = 0, for 1 < t
units for 1 < t < 2s

for 0 < t < 1s
, for 1 < t < 2s
Thus, for 1 < t <2s
For more than 2 seconds

Question:5.37

A racing car travels on a track ABCDEFA. ABC is a circular arc of radius 2 R. CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The coefficient of friction on the road is = 0.1. The maximum speed of the car is 50 m/s. Find the minimum time for completing one round.

Answer:

To keep the car in circular motion centripetal force is provided by frictional force inward to centre O.
(i) Time is taken by the car to travel from A→B→C
Let s1 be the length of the path
Therefore,


The maximum speed of the car along the circular path is

= 14.14 m/s
Thus,
(ii) Time taken by the car to travel from C to D & F to A
s₂ = CD + FA
= R + R
= 200 m
The car will travel with max. speed v₂ i.e., 50 m/s
Thus,

= 4 sec
(iii) Time taken for the path from D to E to F will be






Therefor the total time taken by car =
= 66.62 + 4 +15.7
= 86.32s

Question:5.38

The displacement vector of a particle of mass m is given by

a) show that the trajectory is an ellipse
b) show that

Answer:

For plotting the graph (r-t) or trajectory we relate x & y coordinates.
(a)
&
……… (i)
……… (ii)
On squaring and adding (i) & (ii), we get,



Here, we are getting the equation of an ellipse; hence, the trajectory is an ellipse.
(b) Given:
Therefore,
&
Now,
Therefore
&



Therefore,
Thus, the force acting on particle= ma

Question:5.39

A cricket bowler releases the ball in two different ways
a) giving it only horizontal velocity and
b) giving it horizontal velocity and a small downward velocity.
The speed v_s at the time of release is the same. Both are released at a height H from the ground. Which one will have greater speed when the ball hits the ground? Neglect air resistance.

Answer:

(a)
Thus,
Speed of the ball at ground
(b) Here as well, the total energy of the ball when it hits the ground is
Hence the speed is same for (a) as well as (b).

Question:5.4

There are four forces acting at a point P produced by strings as shown in the figure, which is at rest. Find the forces F₁ and F₂.

Answer:

a = 0 … (since the particles are at rest).
Hence, the resultant force & net components along X & Y axis will also be 0.
Let us resolve all the forces along X-axis,
F_x = 0,


Or,


= 0.707 N
Now let us resolve all the forces along Y-axis
F_y = 0


= 3 (0.707)
= 2.121 N

Question:5.41

A rectangular box lies on a rough inclined surface. The coefficient of friction between the surface and the box is . Let the mass of the box be m.a) at what angle of inclination of the plane to the horizontal will the box just start to slide down the plane?
b) what is the force acting on the box down the plane, if the angle of inclination of the plane is increased to a >
c) what is the force needed to be applied upwards along the plane to make the box either remain stationary or just move up with uniform speed?
d) what is the force needed to be applied upwards along the plane to make the box move up the plane with acceleration a.

Answer:

(a) By angle of repose , as the box start to slide down the plane.
Therefore,
(b) the angle of inclination of the plane with horizontal will slide down if angle , as is the angle of repose.
Thus, the net downward force will be,




(c) To move the box upward with uniform velocity or to keep it stationary,

Or ….. (since a=0)

Therefore,
(d) Let F₃ be the force applied to move the box upward with acceleration a.

Thus,

Question:5.42

A helicopter of mass 2000 kg rises with a vertical acceleration of 15 m/s². The total mass of the crew and passengers is 500 kg. Give the magnitude and direction of the
a) force on the floor of the helicopter by the crew and passengers
b) action of the rotor of the helicopter on the surrounding air
c) force on the helicopter due to the surrounding air

Answer:

Let, M be the mass of the helicopter, M = 2000 kg
m be the mass of the crew and passengers, m = 500 kg
& a be the acceleration of the helicopter with the passengers and crew, a = 15 ms^-2
(a) Force on floor of helicopter = apparent weight
= m (g + a)
= 500 (10 + 15)
Thus F₁= 500 (25)
= 12588N downward
(b)The action rotor of the helicopter which surrounds the air = Reaction force (by Newton’s 3^rd law),
Due to this, the helicopter rises up along with the crew and passengers with acceleration viz.,
15 ms^-1 = (M + m) (g + a).
Thus, the action of the rotor = (2000 + 500) (g + a).
Thus, F₂ = 2500 (10 + 15)
= 2500 (25)
= 62500 N downward.
(c) Let F₃ be the force acting on the helicopter by the reaction force of the surrounding air.
According to Newton’s 3^rd law
F₃ = -Action force
= -62500 N downward or F₃ = + 62500 N upward.