Advertisements
Advertisements
प्रश्न
A block of mass m is kept over another block of mass M and the system rests on a horizontal surface (In the following figure). A constant horizontal force F acting on the lower block produces an acceleration \[\frac{F}{2 \left( m + M \right)}\] in the system, and the two blocks always move together. (a) Find the coefficient of kinetic friction between the bigger block and the horizontal surface. (b) Find the frictional force acting on the smaller block. (c) Find the work done by the force of friction on the smaller block by the bigger block during a displacement d of the system.
Advertisements
उत्तर
(a) \[a = \frac{F}{2 \left( M + m \right)} (\text{ given })\]
The free-body diagrams of both the blocks are shown below:
For the block of mass m,
\[\text{ ma } = \mu_1 R_1 \text{ and } R_1 = \text{ mg }\]
\[ \Rightarrow \mu_1 = \frac{\text{ma }}{R_1}\]
\[ = \frac{F}{2 \left( M + m \right) g}\]
(b)
Frictional force acting on the smaller block,
\[f_1 = \mu_1 R_1 = \frac{F}{2 \left( M + m \right) g} \times mg\]
\[ = \frac{mF}{2 (M + m)}\]
(c) Work done, w = f1s [where s = d]
\[= \frac{mF}{2 \left( M + m \right)} \times d\]
\[ = \frac{mFd}{2 \left( M + m \right)}\]
APPEARS IN
संबंधित प्रश्न
State if the following statement is true or false. Give a reason for your answer.
Work done in the motion of a body over a closed loop is zero for every force in nature.
A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by
`F = -hati+2hatj+3hatkN`
Where `hati,hatj,hatk` are unit vectors along the x-, y- and z-axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis ?
A boy is sitting on a chair placed on the floor of a room. Write as many action-reaction pairs of forces as you can.
Figure shows a boy pulling a wagon on a road. List as many forces as you can which are relevant with this figure. Find the pairs of forces connected by Newton's third law of motion.
When Neils Bohr shook hand with Werner Heisenberg, what kind of force they exerted ?
The force with which the earth attracts an object is called the weight of the object. Calculate the weight of the moon from the following data : The universal constant of gravitation G = 6.67 × 11−11 N−m2/kg2, mass of the moon = 7.36 × 1022 kg, mass of the earth = 6 × 1024 kg and the distance between the earth and the moon = 3.8 × 105 km.
In tug of war, the team that exerts a larger tangential force on the ground wins. Consider the period in which a team is dragging the opposite team by applying a larger tangential force on the ground. List which of the following works are positive, which are negative and which are zero?
(a) work by the winning team on the losing team
(b) work by the losing team on the winning team
(c) work by the ground on the winning team
(d) work by the ground on the losing team
(e) total external work on the two teams.
A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the plane. The motion of the particle takes place in a plane. It follows that
(a) its velocity is constant
(b) its acceleration is constant
(c) its kinetic energy is constant
(d) it moves in a circular path.
No work is done by a force on an object if
(a) the force is always perpendicular to its velocity
(b) the force is always perpendicular to its acceleration
(c) the object is stationary but the point of application of the force moves on the object
(d) the object moves in such a way that the point of application of the force remains fixed.
A box is pushed through 4.0 m across a floor offering 100 N resistance. How much work is done by the resisting force?
Water falling from a 50-m high fall is to be used for generating electric energy. If \[1 \cdot 8 \times {10}^5 \text{ kg } \] of water falls per hour and half the gravitational potential energy can be converted into electrical energy, how many 100 W lamps can be lit with the generated energy?
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 block of mass 1 kg is placed at point A of a rough track shown in figure following. If slightly pushed towards right, it stops at point B of the track. Calculate the work done by the frictional force on the block during its transit from A to B.
A particle of mass m is kept on a fixed, smooth sphere of radius R at a position where the radius through the particle makes an angle of 30° with the vertical. The particle is released from this position. (a) What is the force exerted by the sphere on the particle just after the release? (b) Find the distance travelled by the particle before it loses contact with the sphere.
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 body is being raised to a height h from the surface of earth. What is the sign of work done by applied force?
A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 30° by a force of 10 N parallel to the inclined surface (Figure). The coefficient of friction between block and the incline is 0.1. If the block is pushed up by 10 m along the incline, calulate
- work done against gravity
- work done against force of friction
- increase in potential energy
- increase in kinetic energy
- work done by applied force.
Work done by gas in cyclic process is ______ J.
In the integration method for variable force, why do we divide displacement into tiny segments (ds)?
