A ball of mass m kg is rolled up a slope at an angle θ to the horizontal, where sin θ = 2 5 . The ball passes a point A with speed 7 m s - 1 . A point B is 5 m further up the slope than point A . Find the time between passing $B$ on the way up and returning to B on the way down.

Draw the force-free body diagram as given below Now compare the force values in the parallel to the incline slope - m g sin θ = m a a = - g sin θ = - 2 5 × 10 = - 4 m / s 2 Now use the constant acceleration formula as follows s = u t + 1 2 a t 2 s = 5 m , u = 7 m / s , a = - 4 m / s 2 , t = ? 5 = 7 t - 2 t 2 2 t 2 - 7 t + 5 = 0 2 t - 5 t - 1 = 0 t = 1 s o r 2 . 5 s The ball at B at t = 1 s and t = 2 . 5 s so the timing between passing B on the way up and down is 1 . 5 s .

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Starting from rest, a body slides down a 45° inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is

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Important Questions on Newton's Laws of Motion

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Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

A stone is dropped from the top of a building. When it crosses a point

5 m

below the top, another stone starts to fall from a point

25 m

below the top. Both stones reach the bottom of building simultaneously. The height of the building is :

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Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

A body is projected vertically upwards with a velocity

' u'

from the top of a tower. Time taken by it to reach the ground is

' n'

times the time taken by it to reach the highest point in its path. Height of the tower is

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Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

A person jumps from the

5^{th}

storey of a building with load on his head. The weight experienced by him before reaching the earth will be

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Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

On a smooth plane surface (figure) two block

A

and

B

are accelerated rightwards by applying a force

15 N

A

. If mass of

B

is twice that of

A

, the force on

B

MEDIUM

Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

An object takes

n

times as much time to slide down a

45 °

rough inclined plane as it takes to slide down a perfectly smooth

45 °

inclined plane. The coefficient of kinetic friction between the rough plane and the object is

MEDIUM

Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

An inclined plane making an angle of $30 °$ with the horizontal is placed in a uniform horizontal electric field $200 \frac{N}{C}$ as shown in the figure. A body of mass $1 kg$ and charge $5 mC$ is allowed to slide down from rest at a height of $1 m$ . If the coefficient of friction is $0.2,$ find the time taken by the body to reach the bottom.
$[g = 9.8 m s^{- 2}; \sin 30 ° = \frac{1}{2}; \cos 30 ° = \frac{\sqrt{3}}{2}]$

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Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

A box filled with water has a small hole on its side near the bottom. It is dropped from the top of a tower. As it falls, a camera attached on the side of the box records the shape of the water stream coming out of the hole. The resulting video will show

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Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

A block of mass m is placed on a smooth inclined wedge

A B C

of inclination

θ

as shown in the figure. The wedge is given an acceleration

a

towards the right. The relation between

a

and

θ

for the block to remain stationary on the wedge is

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MEDIUM

Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

Two blocks of masses

m_{1}

and

m_{2}

are suspended by a massless string passing over a smooth pulley. If the acceleration of the system is

\frac{g}{8},

then the ratio of the masses

\frac{m_{2}}{m_{1}} =

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Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

Two blocks $A$ and $B$ of masses $1.5 kg$ and $0.5 kg$ respectively are connected by a massless inextensible string passing over a frictionless pulley as shown in the figure. Block A is lifted until block B touches the ground and then block A is released. The initial height of block A is $80 cm$ when block B just touches the ground. The maximum height reached by block $B$ from the ground after the block A falls on the ground is

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Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

A block of mass

48 kg

kept on a smooth horizontal surface is pulled by a rope of length

4 m

by a horizontal force of

25 N

applied to the other end. If the linear density of the rope is

0.5 kg m^{- 1},

the force acting on the block is

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Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

A ball is thrown vertically downward with a velocity of

20 m s^{- 1}

from the top of a tower. It hits the ground after some time with a velocity of

80 m s^{- 1}

. The height of the tower is:

(g = 10 m s^{- 2})

HARD

Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

A student skates up a ramp that makes an angle $30 °$ with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed $v_{0}$ and wants to turn around over a semicircular path $x y z$ of radius $R$ during which he/she reaches a maximum height $h$ (at point $y$ ) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then ( $g$ is the acceleration due to gravity)

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Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

Two bodies of mass

4 kg

and

6 kg

are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity

(g)

is:

HARD

Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

A $10 m$ long slope makes an angle $30 °$ with the horizontal. $A$ box of mass $8 kg$ is pulled up the slope by a rope that is parallel to the slope. The coefficient of friction between the box and the slope is $\frac{1}{\sqrt{12}} .$ At the top of the slope, the rope passes over a smooth pulley. A ball of mass $12 kg$ hangs from the other end of the rope. The ball is initially $2 m$ above the ground. The system is released from rest.

Find how long it will take for the box to travel $1.5 m$ up the slope.

HARD

Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

A ball of mass

m kg

is rolled up a slope at an angle

θ

to the horizontal, where

\sin θ = \frac{2}{5} .

The ball passes a point

A

with speed

7 m s^{- 1} .

A point

B

5 m

further up the slope than point

A .

Find the time between passing $B$ on the way up and returning to

B

on the way down.

HARD

Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

Particles

A

and

B,

of masses

0.5 kg

and

2.5 kg,

respectively, are attached to the ends of a light inextensible string. Particle A is held on a rough slope. The slope is inclined at

30 °

to the horizontal and the coefficient of friction between the slope and particle A is

0.3 .

The string passes over a small smooth pulley at the top of the slope and particle

B

hangs vertically below the pulley. The length of the slope is

4 m

and the length of the string is

3 m .

Particle

B

1 m

above the ground. Particle A is released and moves up the slope. When particle B reaches the ground the string is cut. Show that particle A does not reach the pulley.

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Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

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A block of mass $60 kg$ is pulled up a hill in the line of greatest slope by a force of magnitude $50 N$ acting at an angle $α °$ above the hill. The block passes through points $A$ and $B$ with speeds $8.5 m s^{- 1}$ and $3.5 m s^{- 1}$ respectively (see diagram). The distance $A B$ is $250 m$ and $B$ is $17.5 m$ above the level of $A .$ The resistance to motion of the block is $6 N .$ Find the value of $α .$

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Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

A block of mass

m

is placed on a smooth inclined plane of inclination

θ

with the horizontal. The force exerted by the plane on the block has a magnitude

HARD

Physics>Mechanics>Newton's Laws of Motion>Applications of Second and Third Laws

A cyclist of mass

70 kg

(including her bicycle) arrives at an uphill stretch of road of length

30 m

with an angle

9 °

to the horizontal, travelling at

10 m s^{- 1} .

She exerts a force of

15 N

parallel to the slope and there is wind resistance of

5 N

against her. Find the time taken to reach the top of the slope.

Starting from rest, a body slides down a 45° inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is

Important Questions on Newton's Laws of Motion

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