 ## 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 kg Initial height (h1) = 1/5 m

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

## 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 : Angle (θ) = 60o

Mass of ball (m) = 0.2 kg

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

Time interval (Δt) = 0.01 second

## Nonuniform linear motion – problems and solutions

Nonuniform linear motion – problems and solutions

1. The table above shows data of three objects that travel the same distance at constant acceleration.

What are the final speed of object P and the initial speed of object Q?

## 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

## Rotation of rigid bodies – problems and solutions

Rotation of rigid bodies – problems and solutions

The moment of force

1. Three forces act on a beam with a length of 6 meters, as shown in the figure below. What is the net torque rotates the beam about the point O as the axis of rotation?

Known : The axis of rotation at point O.

Force 1 (F1) = F

The distance between the line of action of F1 with the axis of rotation (r1) = 3 meters

## 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 m Mass (m) = 160 gram = 0.16 kg

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

## Dynamics of rotational motions – problems and solutions

Dynamics of rotational motions – problems and solutions

1. A pulley with the moment of inertia I = 2/5 MR2 has a mass of 2-kg. If the moment of force on the pulley is 4 N.m then what is the linear acceleration of the pulley. Acceleration due to gravity is g = 10 m.s-2.

Known : The moment of inertia of the pulley (I) = 2/5 MR2

Mass of pulley (M) = 2 kg

Moment of force (τ) = 4 Nm

## 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 kg Mass of object B (mB) = 4 kg

Force (F) = 60 Newton

## 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 = x Part of the object in liquid A = 0.6

The density of liquid A = y

Part of object in liquid B = 0.5

## 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/s 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