what is the speed of a 0.25 kg ball if its kinetic energy is 15J?
The kinetic energy (KE) of an object can be calculated using the equation KE = (1/2)mv^2, where m represents the mass of the object and v represents its velocity.
In this problem, we are given that the kinetic energy of the ball is 15J and the mass of the ball is 0.25 kg.
Using the kinetic energy equation, we can rearrange it to solve for velocity (v):
KE = (1/2)mv^2
15 = (1/2)(0.25)v^2
To solve for v, we first multiply both sides of the equation by 2 to get rid of the fraction:
30 = (0.25)v^2
Then, divide both sides of the equation by 0.25:
120 = v^2
Finally, take the square root of both sides to find v:
v = √120
v ≈ 10.95 m/s
Therefore, the approximate speed of the 0.25 kg ball with a kinetic energy of 15J is about 10.95 m/s.
A boy pushes down on a car rolling horizontally down the road, if the boy pushes down vertically with 10 N of force as rolls 3.0 m horizontally, the amount of work done by the boy is
Work is defined as the product of the force applied in the direction of the displacement and the magnitude of displacement. In this case, the force is applied vertically while the displacement is horizontal. Therefore, the vertical force does not do any work on the car in the horizontal direction.
The work done by the boy can be calculated using the equation:
Work = Force × Displacement × cos(θ)
Where:
Force = 10 N
Displacement = 3.0 m
θ = the angle between the force and displacement vectors (which is 90 degrees in this case)
Since cos(90) = 0, the work done by the boy is:
Work = 10 N × 3.0 m × cos(90)
Work = 10 N × 3.0 m × 0
Work = 0 J
Therefore, the amount of work done by the boy is 0 Joules.
To find the speed of the ball, we can use the formula for kinetic energy:
Kinetic Energy = (1/2) * mass * speed^2
Given:
Mass of the ball (m) = 0.25 kg
Kinetic Energy (KE) = 15 J
Rearranging the formula, we can solve for speed:
speed = √[(2 * KE) / mass]
Plugging in the given values:
speed = √[(2 * 15) / 0.25]
Calculating the numerator:
2 * 15 = 30
Substituting the value:
speed = √[30 / 0.25]
Dividing to get the result:
speed = √120
Simplifying the square root:
speed ≈ 10.95 m/s
Therefore, the speed of the 0.25 kg ball, if its kinetic energy is 15 J, is approximately 10.95 m/s.