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

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==Problem 1==
 
==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?
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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==
 
==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?
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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==
 
==Problem 3==
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==Problem 5==
 
==Problem 5==
An massless object is thrown upwards in a projectile path, at an angle of <math>\theta</math> with a velocity <math>v</math>. What is the maximum height reached by the object?
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A glass hollow sphere with radius <math>r</math> rests on the topmost point of a much larger Woden sphere with radius <math>R</math> and <math>R >> r</math>. The coefficient of kinetic friction between the surfaces is <math>\mu_k</math>. 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?
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==Problem 6==
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A block of mass <math>m</math> initially at rest, is dropped from height <math>h</math> above a spring of spring constant <math>k</math>. What is the maximum compression of the spring?
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==Problem 7==
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Initially, A block <math>A</math> has a mass of <math>14 kg</math> which slides across surface with velocity <math>u</math> and block <math>B</math> has a mass of <math>16 kg</math> which slides at a speed of <math>v</math>, with <math>u > v</math>. Block A slides east while Block B slides in west. The surface has coefficient of friction <math>\mu</math>. How far does do the blocks move together before stopping?

Latest revision as of 11:52, 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?