Advertisements
Advertisements
Question
A 250 g block slides on a rough horizontal table. Find the work done by the frictional force in bringing the block to rest if it is initially moving at a speed of 40 cm/s. If the friction coefficient between the table and the block is 0⋅1, how far does the block move before coming to rest?
Advertisements
Solution
\[\text{ Given } : \]
\[\text{ Mass of the block, m = 250 gm = 0 . 250 kg } \]
\[\text{ Initial speed of the block, u = 40 cm/s = 0 . 4 m/s } \]
\[\text{ Final speed of the block, }\nu = 0 \]
\[\text{ Coefficient of friction, } \mu = 0 . 1\]
Force in the forward direction is equal to the friction force.
\[\text{ Here } , \mu \text{ R = ma } \]
\[\left( \text{ where a is deceleration } \right)\]
\[a = \left( \frac{\mu R}{m} \right) = \left( \frac{\mu \text{ mg }}{m} \right) = \mu \text{ g } \]
\[ = 0 . 1 \times 9 . 8 = 0 . 98 \text{ m/ s} ^2 \]
\[s = \frac{\nu^2 - u^2}{2a} = 0 . 082 \text{ m } \]
\[ = 8 . 2 \text{ cm } \]
Again, work done against friction,
\[W = - \mu \text{ Rs } \cos \theta\]
\[ = - 1 \times 2 . 5 \times 0 . 082 \times 1\]
\[ = - 0 . 02 J\]
\[ \Rightarrow W = - 0 . 02 J\]
APPEARS IN
RELATED QUESTIONS
A body of mass m is placed on a table. The earth is pulling the body with a force mg. Taking this force to be the action what is the reaction?
Let E, G and N represent the magnitudes of electromagnetic gravitational and nuclear forces between two electrons at a given separation. Then
Which of the following systems may be adequately described by classical physics ?
(a) motion of a cricket ball
(b) motion of a dust particle
(c) a hydrogen atom
(d) a neutron changing to a proton.
The gravitational force acting on a particle of 1 g due to a similar particle is equal to 6.67 × 10−17 N. Calculate the separation between the particles.
At what distance should two charges, each equal to 1 C, be placed so that the force between them equals your weight ?
A monkey is sitting on a tree limb. The limb exerts a normal force of 48 N and a frictional force of 20 N. Find the magnitude of the total force exerted by the limb on the monkey.
The work done by all the forces (external and internal) on a system equals the change in ______.
A particle moves from a point \[\overrightarrow{r}_1 = \left( 2 m \right) \overrightarrow{ i } + \left( 3 m \right) \overrightarrow{ j } \] to another point
\[\overrightarrow{r}_2 = \left( 3 m \right) \overrightarrow{ i } + \left( 2 m \right) \overrightarrow{ j } \] acts on it. Find the work done by the force on the particle during the displacement.
A man moves on a straight horizontal road with a block of mass 2 kg in his hand. If he covers a distance of 40 m with an acceleration of 0⋅5 m/s2, find the work done by the man on the block during the motion.
A box weighing 2000 N is to be slowly slid through 20 m on a straight track with friction coefficient 0⋅2 with the box. (a) Find the work done by the person pulling the box with a chain at an angle θ with the horizontal. (b) Find the work when the person has chosen a value of θ, which ensures him the minimum magnitude of the force.
A block of mass 2 kg kept at rest on an inclined plane of inclination 37° is pulled up the plane by applying a constant force of 20 N parallel to the incline. The force acts for one second. Find the work done by the force of gravity in that one second if the work done by the applied force is 40 J.
The 200 m free-style women's swimming gold medal at Seoul Olympics in 1988 was won by Heike Friendrich of East Germany when she set a new Olympic record of 1 minute and 57⋅56 seconds. Assume that she covered most of the distance with a uniform speed and had to exert 460 W to maintain her speed. Calculate the average force of resistance offered by the water during the swim.
A uniform chain of mass m and length l overhangs a table with its two third part on the table. Find the work to be done by a person to put the hanging part back on the table.
A lawn roller is pulled along a horizontal surface through a distance of 20 m by a rope with a force of 200 N. If the rope makes an angle of 60° with the vertical while pulling, the amount of work done by the pulling force is:
A graph of potential energy V(x) verses x is shown in figure. A particle of energy E0 is executing motion in it. Draw graph of velocity and kinetic energy versus x for one complete cycle AFA.
A block of mass m is taken from A to B slowly under the action of a constant force R Work done by this force is ______.
A cylinder of area 300 cm2 and length 10 cm made of material of specific gravity 0.8 is floated in water with its axis vertical. It is then pushed downward, so as to be just immersed. The work done by the agent who pushes the cylinder into the water is ______ J.
Force acting on a particle is (2`hat"i"` + 3 `hat"j"`) N. Work done by this force is zero, when a particle is moved on the line 3y + kx = 5. Here value of k is ______.
In the integration method for variable force, why do we divide displacement into tiny segments (ds)?
What does 'dW' represent in the variable force work calculation?
