Difference between revisions of "F = MA 2020 (Mock) Problems"

Latest revision as of 10:52, 1 August 2020

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?

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 ==Problem 1==
-Initially at rest, <math>2</math> masses <math>3m</math> and <math>5m</math> hang on <math>2</math> ends of a massless rope on a massless, smooth pulley and the mass <math>3m</math> hangs <math>l</math> feet above the ground. Once the system is released, what is the speed of the <math>3m</math> block when it strikes the ground?
+A wire is connected to <math>3</math> blocks lying adjacent to each other. The masses of the 3 blocks have masses <math>4 kg</math>, <math>9 kg</math>, and <math>M</math>. The tension in the wire while pulling the blocks is <math>120</math> newtons and the blocks move with a constant velocity. What is <math>M</math>?
 ==Problem 2==
-An equilateral triangle has a side length of <math>s</math>. How high above the base of the triangle the center of mass of the triangle located?
+A block of mass <math>M</math> moving at a speed of <math>v1</math> collides with another block of mass <math>m</math> which is originally moving at a speed of <math>v2</math>. The block of mass <math>m</math> had a spring attached to the back of it with spring constant <math>k_s</math>. What is the maximum compression of the spring after the collision?
 ==Problem 3==

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