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A projectile is launched at a speed of 20 m/s and at an angle of 25 degrees above the horizontal. What is the maximum height of the projectile?


a photon of yellow light of frequency
5.0 * 10^14Hz is emitted in a time of
10^-8 seconds
evaluate 1. the length of the wave train
2. the number of complete oscillations present in the wave train
Write down equations for the following constraints of mechanical systems
and classify them with respect to whether they are scleronomic or rheonomic and
holonomic or not nonholonomic.
a) A small ball which rolls down on the surface of a big ball without friction.
b) The suspension point of a planar pendulum carries out harmonic horizontal
oscillations.
c) A bead moving freely on a long straight wire through the origin, which rotates
in the x-y plane with constant angular velocity w about the z-axis.
d) A bead slides along a straight wire. The wire has constant inclination a
towards the horizontal x-y-plane and moves with constant acceleration in x
direction.
Let r= r(q1 ... qn, t). The generalized coordinates qi are not necessarily independent. Show that

a) ar/(agi)=ai/(aqi)

b)ai/(aqi) =d/(dt) ar/(aqr)

There's a hanging mass, and a cart attached to it via a string.

1) If the hanging mass is much heavier than the mass of the cart, what would be the acceleration of the system? Explain why.

2) If the hanging mass and the cart were the exact same mass, what would be the acceleration of the system? Explain why.


No values are required! Just a general explanation. Please try to explain in words (Ex. the acceleration would be zero because...) instead of just formulas, it helps me understand better! You may use formulas to represent what you are saying but I'd like a more wordy explanation. Thanks so much.



2. An object is thrown upward and returns to the ground 12 seconds. How high did the ball go?

3. A bus is traveling with a uniform velocity of 20 m/s. At the instant it passes a car at rest, the car starts to accelerate at 4 m/s2 in the same direction as the velocity of the bus. (a) After how many seconds will the car overtake the bus? (b) How far will the car travel before overtaking the bus?

A small collar is confined to travel along a horizontal circular rod of radius 0.35

0.35 m as shown. The coefficient of kinetic friction between the rod and collar is 0.36

At a particular instant the collar is moving at 2.45m/s.  At that instant ...

a) [3] ... what is its rate of change of speed? (Take g = 9.81 m/s2.)    m/s

[Notes: you don't need the mass of the collar; it will cancel. Also, a reminder that the normal force has two components here: a normal/radial component and a binormal component. There is no calculus in this problem.]

b) [1] ... what angle does the normal force the rod exerts on the collar make above the horizontal?   degrees



Question:

There's a hanging mass, and a cart attached to it via a string.

1) If the hanging mass is much heavier than the mass of the cart, what would be the acceleration of the system? Explain why.

2) If the hanging mass and the cart were the exact same mass, what would be the acceleration of the system? Explain why.


No values are required! Just a general explanation. Please use words for an explanation (Ex. the acceleration would be the same because…) instead of just formulas (formulas to represent are ok, but I need it written in pure wording to understand fully) Thanks!


In a game of tug-of-war, the team that pushes the ground harder in a horizontal direction wins. Explain why. You may want to include a sketch


I have a question regarding Newton's 2nd Law.

There's a hanging mass, and a cart attached to it via a string.

1) If the hanging mass is much heavier than the mass of the cart, what would be the acceleration of the system? Explain why.

2) If the hanging mass and the cart were the exact same mass, what would be the acceleration of the system? Explain why.


No values are required! Just a general explanation. Thanks.


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