F = MA 2020 (Mock) Problems

Problem 1

A wire is connected to $3$ blocks lying adjacent to each other. The masses of the 3 blocks have masses $4 kg$, $9 kg$, and $M$. The tension in the wire while pulling the blocks is $120$ newtons and the blocks move with a constant velocity. What is $M$?

Problem 2

A block of mass $M$ moving at a speed of $v1$ collides with another block of mass $m$ which is originally moving at a speed of $v2$. The block of mass $m$ had a spring attached to the back of it with spring constant $k_s$. What is the maximum compression of the spring after the collision?

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?