A 0.38-kg particle has a speed of 2.0 m/s at point A and kinetic energy of 7.5 J at point B.
(a) What is its kinetic energy at A?
J
(b) What is its speed at point B?
m/s
(c) What is the total work done on the particle as it moves from A to B?
a,b) KE= 1/2 mass*v^2
c) the work done is the difference in energies at A,B
To solve this problem, we can use the formula for kinetic energy:
Kinetic energy = (1/2) * mass * speed^2
Let's calculate the answers step by step.
(a) What is its kinetic energy at A?
Given:
Mass (m) = 0.38 kg
Speed at point A (v_A) = 2.0 m/s
To find the kinetic energy at A, we can use the formula for kinetic energy:
Kinetic energy at A = (1/2) * mass * speed^2
Substituting the given values:
Kinetic energy at A = (1/2) * 0.38 kg * (2.0 m/s)^2
Kinetic energy at A = 0.38 * 2.0^2 J
Kinetic energy at A = 0.38 * 4.0 J
Kinetic energy at A = 1.52 J
Therefore, the kinetic energy at point A is 1.52 J.
(b) What is its speed at point B?
Given:
Mass (m) = 0.38 kg
Kinetic energy at point B (K_B) = 7.5 J
To find the speed at point B, we need to rearrange the formula for kinetic energy:
Kinetic energy = (1/2) * mass * speed^2
Solving for speed:
speed = √(2 * kinetic energy / mass)
Substituting the given values:
speed at B = √(2 * 7.5 J / 0.38 kg)
speed at B = √(15 J / 0.38 kg)
speed at B = √(39.47 m^2/s^2)
speed at B ≈ 6.28 m/s
Therefore, the speed at point B is approximately 6.28 m/s.
(c) What is the total work done on the particle as it moves from A to B?
The work done on a particle is given by the change in its kinetic energy.
Change in kinetic energy = Kinetic energy at B - Kinetic energy at A
Substituting the given values:
Change in kinetic energy = 7.5 J - 1.52 J
Change in kinetic energy = 5.98 J
Therefore, the total work done on the particle as it moves from point A to point B is 5.98 J.
To solve this problem, we need to use the formulas for kinetic energy and work done.
(a) To find the kinetic energy at point A, we can use the formula:
Kinetic Energy = 1/2 * mass * velocity^2
Given that the mass of the particle is 0.38 kg and the speed at point A is 2.0 m/s, we can substitute these values into the formula:
Kinetic Energy at A = 1/2 * 0.38 kg * (2.0 m/s)^2
Simplifying this equation:
Kinetic Energy at A = 1/2 * 0.38 kg * 4.0 m^2/s^2
Kinetic Energy at A = 0.38 kg * 2.0 m^2/s^2
Kinetic Energy at A = 0.76 J
So, the kinetic energy at point A is 0.76 J.
(b) To find the speed at point B, we need to rearrange the kinetic energy formula and solve for velocity:
Kinetic Energy = 1/2 * mass * velocity^2
Substituting the given values, we have:
7.5 J = 1/2 * 0.38 kg * velocity^2
Rearranging the equation:
velocity^2 = (7.5 J * 2) / (0.38 kg)
velocity^2 = 39.47 m^2/s^2
Taking the square root of both sides to solve for velocity:
velocity = √(39.47 m^2/s^2)
velocity ≈ 6.28 m/s
So, the speed at point B is approximately 6.28 m/s.
(c) The work done on the particle as it moves from point A to point B is given by the change in kinetic energy. We can calculate it using the formula:
Work = Kinetic Energy at B - Kinetic Energy at A
Substituting the values we found earlier:
Work = 7.5 J - 0.76 J
Work = 6.74 J
So, the total work done on the particle as it moves from A to B is 6.74 J.