Answer:
<u><em>0.03 m/s</em></u>
Explanation:
<em>Applying law of conservation of momentum, </em>
- <em>m₁v₁ + m₂v₂ = (m₁ + m₂)v</em>
- <em>0.105(24) + 75(0) = (0.105 + 75)v</em>
- <em>75.105v = 2.52</em>
- <em>v = 2.52/75.105</em>
- <em>v = </em><u><em>0.03 m/s</em></u>
To solve this exercise it is necessary to take into account the concepts related to Tensile Strength and Shear Strenght.
In Materials Mechanics, generally the bodies under certain loads are subject to both Tensile and shear strenghts.
By definition we know that the tensile strength is defined as

Where,
Tensile strength
F = Tensile Force
A = Cross-sectional Area
In the other hand we have that the shear strength is defined as

where,
Shear strength
Shear Force
Parallel Area
PART A) Replacing with our values in the equation of tensile strenght, then

Resolving for F,

PART B) We need here to apply the shear strength equation, then



In such a way that the material is more resistant to tensile strength than shear force.
Answer:
.7917 m/s
Explanation:
This is a conservation of momentum question. You have an object initially at rest (cart) so that object is initially at 0 momentum. Indiana Jones is 83.5 kg and running 3.75 m/s so he starts with a momentum of 313.125 kg * m/s because momentum is equal to mass * velocity. Once the person jumps in the cart, the cart and the person can be considered one object and by conservation of momentum, the momentum of the Indiana-cart system is equal to 313.125 kg * m/s. By that, we can set that momentum equal to the combined mass * joint velocity. So 313.125 = (83.5kg + 312kg) * joint velocity. Then just solve for the velocity. The answer should be smaller than the intial velocity of the person of 3.75 m/s because the mine cart is HUGE at 312kg.
Explanation:
Given that,
Distance, s = 47 m
Time taken, t = 8.6 s
Final speed of the truck, v = 2.3 m/s
Let u is the initial speed of the truck and a is its acceleration such that :
.............(1)
Now, the second equation of motion is :

Put the value of a in above equation as :




u = 8.63 m/s
So, the original speed of the truck is 8.63 m/s. Hence, this is the required solution.
Answer:
h = 2.64 meters
Explanation:
It is given that,
Mass of one ball, 
Speed of the first ball,
(upward)
Mass of the other ball, 
Speed of the other ball,
(downward)
We know that in an inelastic collision, after the collision, both objects move with one common speed. Let it is given by V. Using the conservation of momentum to find it as :


V = 7.2 m/s
Let h is the height reached by the combined balls of putty rise above the collision point. Using the conservation of energy as :



h = 2.64 meters
So, the height reached by the combined mass is 2.64 meters. Hence, this is the required solution.