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1answer
59 views

Need some help with an easy mechanics question.

The distance between a boy and the shelf is R. He wants to throw a ball of mass m with an initial speed v such that it hits the top of the shelf of a height h. 1) Show that a ball thrown at the ...
0
votes
2answers
61 views

My equations are inconsistent. Could someone help me see the error of my ways?

I'm given the following problem: Now, the following is my attempt at a solution: I have two problems: (1) With my equation for $v$, I end up having to take the log of $0$, which is obviously ...
0
votes
2answers
32 views

Help with basic trigonometric (Physics) problem

I am re-learning basic Physics and I would like to know if I followed the correct steps, so I can continue doing more exercises. The problem says: "A person kicks a ball from the surface of a playing ...
0
votes
0answers
19 views

Small oscillations, Lagrangian about equilibrium

I have a Lagrangian $$ L = \underbrace{\dot{x}^2 + \frac{1}{2}\dot{\theta}^2 + \dot{x}\dot{\theta}\cos\theta}_{\text{kinetic energy}} \underbrace{ - \frac{3}{4}x^2 + \cos\theta}_{\text{-ve potential ...
1
vote
2answers
44 views

Homework - Mechanics [closed]

Just started mechanics and I'm not sure what I'm doing wrong on a question. Car accelerates uniformly from a speed of $50kmh^{-1}$ to a speed of $80kmh^{-1}$ in $20$ seconds. a) calculate the ...
4
votes
2answers
442 views

Parametric equations of cycloid on a Ramp

A small wheel of radius r is situated at the top of a ramp having an angle θ = π/3 rad as it appears in the figure below. At t = 0 the wheel is at rest and then it starts to rotate clockwise in the ...
0
votes
2answers
45 views

Vectors Calculation Question

When two vectors are sketched from a single point, the angle between them is θ. Show that the size of their vector summation is given in the expression: $ \sqrt{A^2 + B^2 +2ABcosθ} $. Any ...
0
votes
1answer
101 views

How to find the angle of elevation and launch speed? [closed]

A particle is projected from a point on level ground with a speed of $u$ meters per second and an angle of elevation $\theta$. The maximum height reached by the particle is $42$ meters above the ...
0
votes
2answers
188 views

Expansion of velocity in polar coordinates using kinetic equations

Why does total energy $$E=\dfrac{1}{2}\mu\mathbf{v}^2+U(r)$$ expand to $$E=\dfrac{1}{2}\mu(\dot{r}^{2}+r^2\dot{\phi}^2)+U(r)?$$ It's some form of the kinetic equations in polar coordinates. I know ...
2
votes
1answer
72 views

Kinematics stone thrown upwards past a point, show the following.

I know I should be able to do this, but I have tried for 3 hours and can't do it. I know its simple but it's driving me mad. A particle is projected vertically upwards with speed $ u_{0}$ and passes ...
0
votes
1answer
3k views

Find magnitude and direction of resultant of three given forces?

Using this diagram: A hot-air balloon is ready for take-off. The diagram shows the balloon, tethered by two ropes AB and CD, reach attached to the balloon and the horizontal ground. The weight of ...
1
vote
1answer
101 views

I tried to solve this problem but I can't.please help me

The kinetic energy & potential energy of a dynamical system are given by $$T = \sum_{i=1}^4 f_i(q_i)\left(\frac{dq_i}{dt}\right)^2$$ $$V =\sum_{i=1}^4 V_i(q_i)$$ where $q_i$'s are generalized ...
2
votes
2answers
156 views

Finding angles of two vectors using simultaneous equations

In a physics problem, I am asked to find the resulting angle of two velocity vectors using each velocity vector's components. For the x-component, I have $m_av_{1ax} = m_av_{2ax} + m_bv_{2bx}$. ...
3
votes
0answers
225 views

system of implicit nonlinear differential equations

Here I have a system of nonlinear differential equations: $ (M+2m)\ddot{x} + m(l_1 \ddot{\theta}_1\cos\theta_1 - l_1\dot{\theta}_1^2\sin\theta_1) + ...
0
votes
1answer
1k views

Find the derivative of $F =$ $(GmM)\over r^2$

Newton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass M on a body of mass m is $F =$ $(GmM)\over r^2$ Where G is the gravitational constant and r is the ...
3
votes
3answers
605 views

What exactly is meant by 'Integrate the Equation of Motion'?

Short Question: if a question says to 'integrate the equation of motion', what does it mean? Long Question: Question: Take a planet of mass $M$ and place a satellite at rest at a distance $R$ ...
0
votes
1answer
169 views

Projectile Question

A smooth spherical object (the first object) is projected horizontally from a point of vertical height $H = 28.71$ metres above horizontal ground with a launch speed (initial velocity) of $u = 22.68 ...
0
votes
3answers
1k views

Calculating time of flight of object (Mechanics - horizontal elevated launch)

I need help with the following question: A smooth spherical object is projected horizontally from a point of vertical height H = 25.78 metres above horizontal ground with a launch speed of u = ...
0
votes
2answers
1k views

Calculating initial velocity (horizontal launch)

I need help for the following question: In a long jump event, an athlete jumps a horizontal distance of 7.56m. The athlete was airborne for 3.04 seconds. The acceleration due to gravity is taken as ...
0
votes
2answers
307 views

Physical System for $x'(t)=\sin (x(t))$

I'm asked to find a system that is modeled (or at least approximated) by $x'(t)=\sin (x(t))$ Differentiate yields $x''(t)=\cos (x(t)) \sin (x(t))$ and integrating (care of Wolfram Alpha ) ...
1
vote
1answer
119 views

Simple Harmonic Motion

A particle moving with simple harmonic motion starts from rest at a distance $3m$ from the center of oscillation. If the period is 2$\pi$ seconds: a) Find the time taken to move to a point $2m$ ...