Mechanics | Relativity Answers

A block of mass M, at rest on a horizontal, frictionless surface, is attached to a rigid support by a spring of force constant k. A bullet of mass m and velocity v strikes the block and remains embedded in the block. Determine, a.) the velocity of the block immediately after the collision and b.) the amplitude of the resulting simple harmonic motion.

A 100g cart slides down a ramp angled 30 degrees above the horizontal and arrives at the bottom with a speed 3m/s. How much mechanical energy is lost as the cart slides down the ramp. find the strength of the frictional force acting on the cart. If the cart collides with a second cart, of mass 200g, at the bottom of the ramp and sticks, find the velocity of the two carts

A basketball player is standing on the floor 10.0 m from the basket .The height of the basket is 3.05 m and he shoots the ball at 40.0 angle with the horizantal from the height of 2.00 m .
A- What is the acceleration of the of the basketball at the heights point in its trajectory ?
B- At what speed must the player throw the basketball so that the ball goes through the hoop without striking the bachboard?

A stone is thrown from the ground upward with an initial velocity of 20 m/s

a- At what time the stone will reach the maximum height?
b- What is the maximum height the stone can reach ?
c- What is the height of the stone from the ground after 3 seconds ?

I solved ( A) and ( B) and I need answer for part ( C )

Answer
A- Vf = Vi + gt
0 = 20 + ( 9.8 m/s2) t
20 + 9.8t = 0
9.8 t = -20 so t = -20/9.8 m/s^2 = 2.04 second

B- Vf^2 = Vi^2 + 2g ( Xf – Xi)
(0)^2 = (20)^2 + 2 ( -9.8 m/s^2) ( Xf – 0)
(20)^2 + 2 (-9.8 m/s^2)(Xf) = 0
400 - 19.6 (Xf) = 0
-19.6 Xf = -400
So Xf = - 400/ -19.6 = 20.4 m

Distinguish between uniform and non uniform acceleration.

John and Janet were moving a heavy crate (with a mass M=250 kg) from their leveled driveway into their garage. Janet was pushing the crate horizontally with a force equal to 1/5 her weight. Her mass is 51 kg. John was pulling the crate with a 500N force at a 30 degree angle with the horizontal. The driveway and the wooden crate have a frictional forcve of 50.0N between them.

a.) total work done on the crate when it moved 45 m.
b.) It took 120 seconds to move the crate, calculate power.

Planet A is 35 light years away from the Earth. An astronaut is traveling to the planet in a speed such that he would not age more than 25 years during the journey.


At what speed must the spaceship travel, in the Earth's reference frame,
so that the astronauts age at most 25 years?

Answer is
v = 8.14c

A BOOK OF WEIGHT 2.5N RESTS ON A HORIZONTAL TABLE TOP AND BY MEANS OF A PENCIL A HORIZONTAL FORCE OF 2N IS APPLIED TO THE BOOK CAUSING IT TO SLIDE.THE FORCE OF FRICTION ON THE SLIDING BOOK IS 1N.
A-DRAW A DIAGRAM OF THE SET UP TO SHOW THE BOOK AT REST ON THE TABLE TOP AND FORCES ACTED ON THE BOOK BEFORE THE PENCIL WAS USED.
B-NAME AND GIVE THE MAGNITUDE OF EACH FORCE ACTING ON THE BOOK BEFORE THE FORCE WAS APPLIED WITH THE PENCIL.
C-WRITE A BRIEF EXPLANATION FOR THE STAE OF REST OF THE BOOK.
D-DRAW A SEPARATE DIAGRAM TO SHOW THE SLIDING BOOK AND THE FORCES ACTED ON IT.
E-CALCULATE THE VELOCITY OF THE BOOK WHEN THE APPLIED FORCE HAS BEEN ACTING ON IT FOR 1.5 SECONDS.
USE GRAVITY=10 (N/KG)

A motor car starts moving at A and moves to B by uniform acceleration.It moves B to C by uniform velocity that has a value of 10m/s and moves C to D by uniform retardation and stops.It takes 35s to move A to D and BC=200m.Draw a velocity time graph for the motion of car.(the motor car starts with motionless and it moves in a straight way)
1.what is the car's acceleration?
2.what time period it moves by acceleration?
3.mention the distance that the car moves by acceleration.
4.mention the distance that the car moves by retardation.

The driver loses control of the car when driving at sharp corner at high speed. What are the safety features need to install the situation?