TutorMe homepage
Subjects
PRICING
COURSES
SIGN IN
Start Free Trial
Paul H.
Former assistant Judo instructor and Boy Scout mentor
Tutor Satisfaction Guarantee
French
TutorMe
Question:

Decrivez votre chambre en utilisant le vocabulaire appris en cours. (Negligez les accents)

Paul H.
Answer:

Ma chambre est tres petite. Mon lit est a cote de mon etagere. J'ai beaucoup de livres dedans. En face de l'etagere j'ai un bureau. C'est la que je fais mes devoirs. En-dessous de mon lit j'ai des vetements et mon materiel de sport.

Calculus
TutorMe
Question:

Two trains leave from the same point. One leaves at noon going east at a constant 10mph. The other leaves at 1 pm going south at a constant 15mph. How fast is the distance between the two trains changing at 5 pm?

Paul H.
Answer:

Let c be the distance between the trains. At any time t, using the Pythagorean theorem, the distance between the trains can be expressed as: c^2=(10 t)^2+(15 (t-1))^2 (The "t-1" term is due to the fact that the second train leaves an hour later than the first) To obtain the rate of change, we'll take the time derivative of both sides. d/dt [c^2] = d/dt [(10 t)^2+(15 (t-1))^2] using the chain rule, 2c * d/dt[c] = 2*(10 t) * d/dt[10 t] + 2*(15 (t-1)) * d/dt[[15 (t-1)] c * d/dt[c] = (10 t) * 10 + (15 (t-1)) * 15 c * d/dt[c] = 100 t + 225(t-1) d/dt[c] = {100 t + 225(t-1)}/c at t=5, c^2=6100 miles so c=78.10 miles Plugging in these values, d/dt[c] = {100*5 + 225(5-1)}/78.10 d/dt[c] =17.9 mph

Physics
TutorMe
Question:

There is a solid sphere of radius R and mass m at the top of a slope of angle 60 degrees. The sphere initially at rest, begins to roll down the hill in a straight line without slipping. Ignore the dragging force on the sphere due to friction. A) What is the kinetic energy of the sphere after it rolls a distance d? B) What is the speed of the sphere at this time?

Paul H.
Answer:

A) Due to the conservation of mechanical energy, the potential energy of the sphere at the top of the slope will be equal to the kinetic energy of the sphere after it travels a distance d. We, therefore, need to calculate the potential energy of the sphere at the top of the slope. Potential energy U=mgh We can set h to be the difference between the initial height of the sphere at the top of the slope and its height after rolling a distance d. Therefore, h=dsin(60) Because of conservation of energy, U(top)=KE(bottom). KE(bottom)=mghsin(60) B) We can calculate the speed of the sphere from the kinetic energy. However, the sphere's total kinetic energy is equal to the sum of translational kinetic energy and rotational kinetic energy. KE(bottom)= 1/2 m v^2 + 1/2 I ω^2 Since the sphere does not slip, we can easily express ω in terms of v. Simply, v=Rω Thus, KE(bottom)=1/2 v^2 (m+I/(R^2))=mgdsin(60) Thus, v^2=2mgdsin(60)/[m+I/(R^2)] The moment of inertia of a solid sphere is I=2m(R^2)/5 v=Sqrt{2mgdsin(60)/[7m/5]} =Sqrt{10gdsin(60)/7}

Send a message explaining your
needs and Paul will reply soon.
Contact Paul
Ready now? Request a lesson.
Start Session
FAQs
What is a lesson?
A lesson is virtual lesson space on our platform where you and a tutor can communicate. You'll have the option to communicate using video/audio as well as text chat. You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.
How do I begin a lesson?
If the tutor is currently online, you can click the "Start Session" button above. If they are offline, you can always send them a message to schedule a lesson.
Who are TutorMe tutors?
Many of our tutors are current college students or recent graduates of top-tier universities like MIT, Harvard and USC. TutorMe has thousands of top-quality tutors available to work with you.