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Collision and conservation of mechanical energy – probems and solutions

Collision and conservation of mechanical energy – probems and solutions

1. Two objects have the same mass, m1 = m2 = 0.5 kg dropped from the same height as shown in the figure below. The radius of the circle is 1/5 m. The collision between both objects is perfectly elastic. Determine the velocity of each object after the collision. Acceleration due to gravity is 10 m/s2.

Known :

Mass of object (m) = m1 = m2 = 0.5 kgCollision and conservation of mechanical energy – probems and solutions 1

Initial height (h1) = 1/5 m

Final height (h2) = 0 (base of path)

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Momentum Impulse and Projectile motion – Problems and Solutions

Momentum Impulse and Projectile motion – Problems and Solutions

1. A 0.2-kg ball will be inserted into hole C, as shown in the figure below. Hitter strikes the ball in 0.01 second and the path of B-C traveled in 1 second. Determine the magnitude of the force so the ball can be inserted into hole C. Acceleration due to gravity is 10 m/s2.

Known :Momentum, impulse and projectile motion - problems and solutions 1

Angle (θ) = 60o

Mass of ball (m) = 0.2 kg

Acceleration due to gravity (g) = 10 m/s2

Time interval (Δt) = 0.01 second

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Kinetic theory of gas and first law of thermodynamics – problems and solutions

Kinetic theory of gas and first law of thermodynamics – problems and solutions

1. Ideal gases are in a container with a volume of 4 liters and its pressure is 3 atm (1 atm = 105 N.m-2). The ideal gases heated at a constant pressure from 27oC to 87oC. The heat capacity of the gas is 9 J.K-1. What is the final volume of gases and the change of internal energy of gases?

Solution

Isobaric process (constant pressure)

Known :

The initial volume of gas (V1) = 4 liters

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Springs in series and parallel – problems and solutions

Springs in series and parallel – problems and solutions

1. A 160-gram object attaches at one end of a spring and the change in length of the spring is 4 cm. What is the change in length of three springs connected in series and parallel, as shown in the figure below?

Known :

The change in length of a spring (Δx) = 4 cm = 0.04 mSprings in series and parallel – problems and solutions 1

Mass (m) = 160 gram = 0.16 kg

Acceleration due to gravity (g) = 10 m/s2

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Dynamics of particles – problems and solutions

Dynamics of particles – problems and solutions

1. Object A with a mass of 6-kg and object B with a mass of 4-kg connected by a cord and pulled by a force of F = 60 N, as shown in the figure below. The coefficient of kinetic friction between the floor and both objects is 0.5 (tan θ = ¾). Acceleration due to gravity is 10 m/s2. What is the magnitude of the tension force?

Known :

Mass of object A (mA) = 6 kgDynamics of particles – problems and solutions 1

Mass of object B (mB) = 4 kg

Force (F) = 60 Newton

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Density and floating in equilibrium – problems and solutions

Density and floating in equilibrium – problems and solutions

1. A block placed into two liquids with different types. In liquids A, 0.6 part of an object is in the liquid. In liquids B, 0.5 part of an object is in the liquid. Determine the ratio of the density of liquid A to liquid B.

Known :

Density of block = xDensity and floating in equilibrium – problems and solutions 1

Part of the object in liquid A = 0.6

The density of liquid A = y

Part of object in liquid B = 0.5

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Conservation of mechanical energy on curve surface – problems and solutions

Conservation of mechanical energy on curve surface – problems and solutions

1. If ball’s speed at point A is 6 m/s, ball’s speed at point B is √92 m/s, and acceleration due to gravity is g = 10 m/s2. What is the height of point B (h)?

Known :

Speed of ball at point A (vA) = 6 m/sConservation of mechanical energy on curve surface – problems and solutions 1

Speed of ball at point B (vB) = √92 m/s

Acceleration due to gravity (g) = 10 m/s2

The height of A (hA) = 5.6 meters

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