Advertisements
Advertisements
Question
In the following figure shows a small block of mass m kept at the left end of a larger block of mass M and length l. The system can slide on a horizontal road. The system is started towards right with an initial velocity v. The friction coefficient between the road and the bigger block is μ and that between the block is μ/2. Find the time elapsed before the smaller blocks separates from the bigger block.
Solution
Let a1 and a2 be the accelerations of masses m and M, respectively.
Also, a1 > a2 so that mass m moves on mass M.
Let after time t, mass m is separated from mass M.
Using the equation of motion
During this time, mass m covers `ct+1/2a_1t^2` and `s_m=vt+1/2a_2t^2`.
For mass m to separate from mass M, we have: `vt+1/2a_1t^2 = vt+1/2a_2t^2+1` ........(ii)
From the free body diagram, we have:
`ma_1+mu/2"R"=0`
`=>ma_1=-(mu/2)"mg"=(mu/2)mxx10`a1 = - 5µ
Again,
`Ma_2+mu("M""m")g-(mu/2)mg=0`
⇒ 2Ma2 + 2μ (M + m)g − μmg = 0
⇒ 2Ma2 = μmg − 2μmg − 2μmg
`=> a_2=(-mumg-2muMg)/(2M)`
Substituting the values of a1 and a2 in equation (i), we get:
`t = sqrt(4Ml)/((M+m)mug)`
APPEARS IN
RELATED QUESTIONS
In a situation the contact force by a rough horizontal surface on a body placed on it has constant magnitude. If the angle between this force and the vertical is decreased, the frictional force between the surface and the body will
The contact force exerted by a body A on another body B is equal to the normal force between the bodies We conclude that
(a) the surface must be frictionless
(b) the force of friction between the bodies is zero
(c) the magnitude of normal force equal that of friction
(d) the bodies may be rough but they don't slip on each other.
Mark the correct statements about the friction between two bodies.
(a) Static friction is always greater than the kinetic friction.
(b) Coefficient of static friction is always greater than the coefficient of kinetic friction.
(c) Limiting friction is always greater than the kinetic friction.
(d) Limiting friction is never less than static friction.
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.
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?
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.
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 coefficient between a road and the type of a vehicle is 4/3. Find the maximum incline the road may have so that once had brakes are applied and the wheel starts skidding, the vehicle going down at a speed of 36 km/hr is stopped within 5 m.
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?
In the following figure shows two blocks in contact sliding down an inclined surface of inclination 30°. The friction coefficient between the block of mass 2.0 kg and the incline is μ1, and that between the block of mass 4.0 kg and incline is μ2. Calculate the acceleration of the 2.0 kg block if (a) μ1 = 0.20 and μ2 = 0.30, (b) μ1 = 0.30 and μ2 = 0.20. Take g = 10 m/s2.
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 acceleration of the block of mass M in the situation of figure in the following. The coefficient of friction between the two blocks is μ1 and that between the bigger block and the ground is μ2.
A block of mass 2 kg is pushed against a rough vertical wall with a force of 40 N, coefficient of static friction being 0.5. Another horizontal force of 15 N, is applied on the block in a direction parallel to the wall. Will the block move? If yes, in which direction? If no, find the frictional force exerted by the wall on the block.
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.
An inclined plane is bent in such a way that the vertical cross-section is given by Y = `x^2/4` where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction µ = 0.5, the maximum height in cm at which a stationary block will not slip downward is ______ cm.
