Advertisements
Advertisements
प्रश्न
Consider the situation shown in the following figure. Calculate (a) the acceleration of the 1.0 kg blocks, (b) the tension in the string connecting the 1.0 kg blocks and (c) the tension in the string attached to 0.50 kg.
उत्तर
From the above diagrams:
T + ma − mg = 0
T + 0.5a − 0.5 g = 0 (1)
μR + ma + T1 − T = 0
μR + 1a + T1 − T = 0 (2)
μR + 1a − T1 = 0
μR + a = T1 (3)
From Equations (2) and (3) we have
μR + a = T − T1
⇒ T − T1 = T1
⇒ T = 2T1
So, Equation (2) becomes
μR + a + T1 − 2T1 = 0
⇒ μR + a − T1 = 0
⇒ T1 = μR + a
= 0.2g + a (4)
and Equation (1) becomes
2T1 + 0.5a − 0.5g = 0
`=> T_1=(0.5g-0.5a)/2`
= 0.25g - 0.25a (5)
From Equations (4) and (5)
0.2g + a = 0.25g − 0.25a
`=>a=0.05/1.25xx10`
= 0.4 x 10 m/s2 [g = 10 m/s2]
Therefore,
(a) the acceleration of each 1 kg block is 0.4 m/s2,
(b) the tension in the string connecting the 1 kg blocks is
T1 = 0.2g + a + 0.4 = 2.4 N
and
(c) the tension in the string attached to the 0.5 kg block is
T = 0.5g − 0.5a
= 0.5 × 10 − 0.5 × 0.4
= 4.8 N.
APPEARS IN
संबंधित प्रश्न
A block A kept on an inclined surface just begins to slide if the inclination is 30°. The block is replaced by another block B and it is found that it just begins to slide if the inclination is 40°.
Let F, FN and f denote the magnitudes of the contact force, normal force and the friction exerted by one surface on the other kept in contact. If none of these is zero.
(a) F > FN
(b) F > f
(c) FN > f
(d) FN − f < F < FN + f.
A block is placed on a rough floor and a horizontal force F is applied on it. The force of friction f by the floor on the block is measured for different values of F and a graph is plotted between them.
(a) The graph is a straight line of slope 45°.
(b) The graph is a straight line parallel to the F-axis.
(c) The graph is a straight line of slope 45° for small F and a straight line parallel to the F-axis for large F.
(d) There is a small kink on the graph.
A block slides down an inclined surface of inclination 30° with the horizontal. Starting from rest it covers 8 m in the first two seconds. Find the coefficient of kinetic friction between the two.
Repeat part (a) of problem 6 if the push is applied horizontally and not parallel to the incline.
A body starts slipping down an incline and moves half metre in half second. How long will it take to move the next half metre?
The angle between the resultant contact force and the normal force exerted by a body on the other is called the angle of friction. Show that, if λ be the angle of friction and μ the coefficient of static friction λ ≤ tan−1 μ.
If the tension in the string in the following figure is 16 N and the acceleration of each block is 0.5 m/s2, find the friction coefficients at the two contact with the blocks.
The friction co-efficient between the table and the block shown in the following figure is 0.2. Find the tensions in the two strings.
The friction coefficient between an athelete's shoes and the ground is 0.90. Suppose a superman wears these shoes and races for 50 m. There is no upper limit on his capacity of running at high speeds. (a) Find the minimum time that he will have to take in completing the 50 m starting from rest. (b) Suppose he takes exactly this minimum time to complete the 50 m, what minimum time will he take to stop?
Two masses M1 and M2 are connected by a light rod and the system is slipping down a rough incline of angle θ with the horizontal. The friction coefficient at both the contacts is μ. Find the acceleration of the system and the force by the rod on one of the blocks.
The friction coefficient between the board and the floor shown in the following figure is μ. Find the maximum force that the man can exert on the rope so that the board does not slip on the floor.
A 2 kg block is placed over a 4 kg block and both are placed on a smooth horizontal surface. The coefficient of friction between the block is 0.20. Find the acceleration of the two blocks if a horizontal force of 12 N is applied to (a) the upper block, (b) the lower block. Take g = 10 m/s2.
Find the accelerations a1, a2, a3 of the three blocks shown in the following figure if a horizontal force of 10 N is applied on (a) 2 kg block, (b) 3 kg block, (c) 7 kg block. Take g = 10 m/s2.
The friction coefficient between the two blocks shown in the following figure is μ but the floor is smooth. (a) What maximum horizontal force F can be applied without disturbing the equilibrium of the system? (b) Suppose the horizontal force applied is double of that found in part (a). Find the accelerations of the two masses.
Consider the situation shown in the following figure. Suppose a small electric field E exists in the space in the vertically charge Q on its top surface. The friction coefficient between the two blocks is μ but the floor is smooth. What maximum horizontal force F can be applied without disturbing the equilibrium?
[Hint: The force on a charge Q bye the electric field E is F = QE in the direction of E.]
A person (40 kg) is managing to be at rest between two vertical walls by pressing one wall A by his hands and feet and the other wall B by his back (in the following figure). Assume that the friction coefficient between his body and the walls is 0.8 and that limiting friction acts at all the contacts. (a) Show that the person pushes the two wall with equal force. (b) Find the normal force exerted by either wall on the person. Take g = 10 m/s2.
The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhered to the wall will be ______ N. [g = 10 ms-2]
