F = MA 2020 (Mock) Problems

Problem 1

Initially at rest, $2$ masses $3m$ and $5m$ hang on $2$ ends of a massless rope on a massless, smooth pulley and the mass $3m$ hangs $l$ feet above the ground. Once the system is released, what is the speed of the $3m$ block when it strikes the ground?

Problem 2

An equilateral triangle has a side length of $s$ . How high above the base of the triangle the center of mass of the triangle located?

Problem 3

A small object of mass $m$ is tied to a string of length $l$ and is whirled around a horizontal circle of radius $r$ with a constant speed $v$ , in a conical pendulum. The center of the circle is vertically below the point of support. What is the period of revolution?

Problem 4

$2$ blocks are connected by a massless string which slide down an inclined plane having an angle of inclination of $40^\circ$ . The masses of the blocks are $M1 = 4 kg$ and $M2 = 2kg$ , and $M1$ is above $M2$ . Both blocks have a Coefficients of friction $0.25$ with the inclined plane. What is the tension in the string?

Problem 5

A glass hollow sphere with radius $r$ rests on the topmost point of a much larger Woden sphere with radius $R$ and $R >> r$ . The coefficient of kinetic friction between the surfaces is $\mu_k$ . The smaller sphere is given a kick down the sphere. At what distance from the top will the smaller sphere lose contact with the larger sphere?

Problem 6

A block of mass $m$ initially at rest, is dropped from height $h$ above a spring of spring constant $k$ . What is the maximum compression of the spring?

Problem 7

Initially, A block $A$ has a mass of $14 kg$ which slides across surface with velocity $u$ and block $B$ has a mass of $16 kg$ which slides at a speed of $v$ , with $u > v$ . Block A slides east while Block B slides in west. The surface has coefficient of friction $\mu$ . How far does do the blocks move together before stopping?

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