A point particle of mass m is attached to a massless string of length L. The oth

Question

A point particle of mass m is attached to a massless string of length L. The other end of the string is attached to a fixed pivot point. The particle moves in a vertical circle under the influence of gravity. The velocity of the particle at a particular instant of time indicated in the figure. If the speed v of the particle at theta = 90 degree is half of the speed V_0 at theta = 0, then v_0 =_________. squareroot gL squarerroot 2gL squarerroot8gL/3 squarerroot 3gL/2 squarerroot 3gL Which of the following situations is impossible? An object has constant non-zero acceleration and changing velocity. An object has constant non-zero velocity and changing acceleration. An object has velocity directed east and acceleration directed east. An object has velocity directed east and acceleration directed north. An object has zero velocity but non-zero acceleration. A uniform ladder of mass 12 kg rests against a wall as shown, making an angle theta with respect to the wall. There is no friction between the wall and the ladder, but the coefficient of static friction between the ladder and the floor is mu_s = 0.42. What is the maximum angle theta such that the ladder does not slip? 40 degree 28 degree 57 degree 35 degree 21 degree

Explanation / Answer

Hi,

In this case I assume you want the answers to questions 59 and 60, as these are the ones that can be clearly seen. If that is the case, then we have the following:

59. Here I consider that the impossible situation is letter B because even if we have situations where the velocity is constant and there is a constant acceleration (uniform circular movement), a situation where the acceleration is not constant while the velocity remains the same is too difficult.

For the other options, I think the following:

Letter A. This is actually a very common situation, an example of this is the free fall.

Letter C. This is another very common situation where the acceleration and the velocity have the same sense and direction. You can imagine a car going to the east while the driver accelerates it.

Letter D. This is not as common, but it can happen. The velocity and the acceleration not always have the same direction, this can be seen in the uniform circular movement, where the acceleration is perpendicular to the velocity.

Letter E. This happens for an instant when you have an object travelling with a certain initial speed that has opposite sense with a certain acceleration. In the end the object will go in the same sense that the acceleration and the point when the change in sense is produced, the velocity of the object is zero.

60. In this case we can solve the problem using the conditions of equilibrium:

Balance of forces over the ladder:                                        Balance of torques over the ladder:

x axis:     fs = R        y axis: mg = N                       mg(L/2) sin() - RL cos() = 0

The condition for the maximum angle is that fs = us N = us mg ; therefore, if we apply the equations we have that the value of is:

R = us mg ::::::::::: (1/2) sin() - us cos() = 0 :::::::: tan() = 2us = 2*0.42 = 0.84 :::::: = 40 °

The answer is Letter A.

Note: in the case of the problem 58 I think it can be done through conservation of energy, but I would need The image to solve it properly.

I hope it helps.

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