1) A 2.5kg durian falls from a tree with a height of 30m. Determine the energy before it falls in Joule.
2) A 2.5kg durian falls from a tree with a height of 30m. Determine the velocity when it drops 20m from the ground.
3) A 2.5kg durian falls from a tree with a height of 30m. Determine the velocity when it hits the ground.
4) A billiard ball of mass 120g is moving with a constant velocity of 1.5ms-1. It strikes a smaller ball and is slowed down to 1.1ms-1. What is the change in momentum of the ball?
5) A billiard ball of mass 120g is moving with a constant velocity of 1.5ms-1. It strikes a smaller ball and is slowed down to 1.1ms-1. If the contact time for the collision is 0.16s, what is the average force acting on the large ball by the small ball?
6) A wheel 25.0cm in radius turning at 120rpm increases its frequency to 600rpm in 9.0s. Find the constant angular acceleration in rads-2.
7) A 180kN tensile force is applied to a metal wire of length 2cm and radius 40mm. If it's elongation is 0.05mm, calculate the tensile stress.
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1) The potential energy of the durian can be calculated using the formula: potential energy (PE) = mass (m) * acceleration due to gravity (g) * height (h).
PE = 2.5kg * 9.8m/s^2 * 30m = 735 Joules.
2) The potential energy at a height of 20m can be calculated using the same formula as in question 1.
PE = 2.5kg * 9.8m/s^2 * 20m = 490 Joules.
To determine the velocity at this height, we can use the equation for gravitational potential energy being converted to kinetic energy: PE = KE.
KE = mv^2 / 2
where m is the mass and v is the velocity.
Rearranging the equation, we can solve for v: v = √(2 * KE / m).
v = √(2 * 490 J / 2.5 kg) = √(196 m^2/s^2) = 14 m/s.
3) When the durian hits the ground, its potential energy is fully converted to kinetic energy. Therefore, we can use the same formula for potential energy to calculate the kinetic energy at this point: PE = KE.
PE = 735 Joules.
KE = 735 Joules.
Using the equation for kinetic energy: KE = mv^2 / 2.
Rearranging the equation, we can solve for v: v = √(2 * KE / m).
v = √(2 * 735 J / 2.5 kg) = √(588 m^2/s^2) = 24 m/s.
4) The change in momentum of the ball can be calculated using the formula: change in momentum (Δp) = mass (m) * change in velocity (Δv).
Δp = 0.120 kg * (1.1 m/s - 1.5 m/s) = -0.048 kg*m/s.
5) The average force acting on the large ball by the small ball can be calculated using the impulse-momentum equation: impulse (J) = force (F) * change in time (Δt).
Impulse can also be calculated as the change in momentum, so J = Δp.
Therefore, F * Δt = Δp.
Rearranging the equation to solve for force, we get: F = Δp / Δt.
F = -0.048 kg*m/s / 0.16 s = -0.3 N (assuming the negative sign indicates the direction of force).
6) The change in angular velocity can be calculated using the formula: change in angular velocity (Δω) = final angular velocity (ωf) - initial angular velocity (ωi).
Δω = (600 rpm - 120 rpm) * (2π radians / 1 minute) * (1 minute / 60 seconds).
Δω = 8π radians/second.
The time taken (Δt) is given as 9.0 seconds.
The constant angular acceleration (α) can be calculated using the formula: α = Δω / Δt.
α = 8π radians/second / 9.0 seconds = 8π/9 radians/second^2.
7) The tensile stress can be calculated using the formula: tensile stress (σ) = force (F) / area (A).
The force applied is 180 kN, which is equivalent to 180,000 N.
The area can be calculated using the formula: area (A) = π * radius^2 = π * (0.04 m)^2 = 0.005 m^2.
σ = 180,000 N / 0.005 m^2 = 36,000,000 N/m^2 or Pa.
1) To determine the energy before the durian falls, we can use the concept of gravitational potential energy. The formula to calculate gravitational potential energy is:
Gravitational potential energy = mass * acceleration due to gravity * height
Given that the mass of the durian is 2.5kg, the acceleration due to gravity is approximately 9.8 m/s², and the height is 30m, we can substitute these values into the formula:
Gravitational potential energy = 2.5kg * 9.8 m/s² * 30m
Gravitational potential energy = 735 Joules
Therefore, the energy before the durian falls is 735 Joules.
2) To determine the velocity when the durian drops 20m from the ground, we can use the principle of conservation of energy. At this point, all the initial potential energy has been converted into kinetic energy. The formula to calculate kinetic energy is:
Kinetic energy = 0.5 * mass * velocity²
We know the mass of the durian is 2.5kg, and we need to find the velocity. We can set up an equation using the conservation of energy principle:
Initial potential energy = Final kinetic energy
mass * acceleration due to gravity * initial height = 0.5 * mass * final velocity²
Substituting the known values:
2.5kg * 9.8 m/s² * 30m = 0.5 * 2.5kg * final velocity²
735 Joules = 1.25kg * final velocity²
Now we can solve for the final velocity by rearranging the equation:
final velocity² = 735 Joules / 1.25kg
final velocity² = 588 m²/s²
final velocity ≈ 24.25 m/s
Therefore, the velocity when the durian drops 20m from the ground is approximately 24.25 m/s.
3) To determine the velocity when the durian hits the ground, we can once again use the principle of conservation of energy. At this point, all the initial potential energy has been converted into kinetic energy. Using the same equation as in the previous explanation:
mass * acceleration due to gravity * initial height = 0.5 * mass * final velocity²
Substituting the known values:
2.5kg * 9.8 m/s² * 30m = 0.5 * 2.5kg * final velocity²
735 Joules = 1.25kg * final velocity²
Now we can solve for the final velocity by rearranging the equation:
final velocity² = 735 Joules / 1.25kg
final velocity² = 588 m²/s²
final velocity ≈ 24.25 m/s
Therefore, the velocity when the durian hits the ground is approximately 24.25 m/s.
4) The change in momentum of the ball can be calculated using the formula:
Change in momentum = final momentum - initial momentum
The formula for momentum is:
Momentum = mass * velocity
Given that the mass of the billiard ball is 120g (which is equivalent to 0.12kg), the initial velocity is 1.5m/s, and the final velocity is 1.1m/s, we can calculate the initial and final momentum:
Initial momentum = 0.12kg * 1.5m/s = 0.18 kg*m/s
Final momentum = 0.12kg * 1.1m/s = 0.132 kg*m/s
Now we can calculate the change in momentum:
Change in momentum = 0.132 kg*m/s - 0.18 kg*m/s
Change in momentum = -0.048 kg*m/s
Therefore, the change in momentum of the ball is -0.048 kg*m/s.
5) Average force can be calculated using the formula:
Average force = change in momentum / contact time
Given that the change in momentum is -0.048 kg*m/s (as calculated in the previous explanation) and the contact time is 0.16s, we can substitute these values into the formula:
Average force = -0.048 kg*m/s / 0.16 s
Average force = -0.3 N (rounded to one decimal place)
Therefore, the average force acting on the large ball by the small ball is approximately -0.3 N (negative sign indicates direction).
6) The formula to calculate angular acceleration is:
Angular acceleration = (final angular velocity - initial angular velocity) / time
To find the angular acceleration, we need to convert the given values from RPM (revolutions per minute) to rad/s. Recall that:
1 revolution = 2π radians
So, for the initial angular velocity, we have:
Initial angular velocity = 120 revolutions/minute * 2π radians/revolution * 1/60 minutes/second
Initial angular velocity = 4π rad/s
For the final angular velocity, we have:
Final angular velocity = 600 revolutions/minute * 2π radians/revolution * 1/60 minutes/second
Final angular velocity = 20π rad/s
Given that the time taken is 9.0 seconds, we can substitute these values into the formula:
Angular acceleration = (20π rad/s - 4π rad/s) / 9.0s
Angular acceleration = 16π rad/s / 9.0s
Angular acceleration ≈ 5.60 rad/s²
Therefore, the constant angular acceleration is approximately 5.60 rad/s².
7) The formula to calculate tensile stress is:
Tensile stress = force / cross-sectional area
Given that the applied force is 180kN (which is equivalent to 180,000N), the length of the wire is 2cm (which is equivalent to 0.02m), the radius is 40mm (which is equivalent to 0.04m), and the elongation is 0.05mm (which is equivalent to 0.00005m), we can calculate the cross-sectional area of the wire:
Cross-sectional area = π * radius²
Cross-sectional area = π * (0.04m)²
Cross-sectional area ≈ 0.005m²
Now we can substitute the force and cross-sectional area into the formula:
Tensile stress = 180,000N / 0.005m²
Tensile stress ≈ 36,000,000 N/m²
Therefore, the tensile stress is approximately 36,000,000 N/m².