A 0.60 kg rubber ball has a speed of 2.0 m/s at point A and kinetic energy of 6.0 J at point B.
(a) Determine the ball's kinetic energy at A.
J
(b) Determine the total work done on the ball as it moves from A to B.
J
(a) You know the formula for kinetic energy (KE). They tell you M and V. Apply the formula at A.
(b) The wrk done on the ball is the increase in KE from A to B.
To solve this problem, we need to use the equation for kinetic energy (KE), which is given by:
KE = (1/2) * m * v^2
where m is the mass of the object and v is its velocity.
(a) To determine the ball's kinetic energy at point A, we can use the given mass and speed.
We can substitute the values into the equation:
m = 0.60 kg
v = 2.0 m/s
KE = (1/2) * m * v^2
= (1/2) * 0.60 kg * (2.0 m/s)^2
= 0.60 kg * 2.0 m^2/s^2
= 0.60 kg * 4.0 J
= 2.4 J
Therefore, the ball's kinetic energy at point A is 2.4 J.
(b) To determine the total work done on the ball as it moves from point A to B, we need to use the work-energy theorem. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
In this case, the initial kinetic energy at point A is 2.4 J, and the final kinetic energy at point B is given as 6.0 J. Therefore, the change in kinetic energy is:
ΔKE = KE_B - KE_A
= 6.0 J - 2.4 J
= 3.6 J
The total work done on the ball as it moves from A to B is equal to the change in kinetic energy, so the answer is 3.6 J.
To solve this problem, we can use the formulas for kinetic energy and work.
(a) The formula for kinetic energy is K.E. = (1/2) * mass * velocity^2. Plugging in the given values, we can solve for the kinetic energy at point A:
K.E. at A = (1/2) * 0.60 kg * (2.0 m/s)^2
K.E. at A = 0.60 J
Therefore, the ball's kinetic energy at point A is 0.60 J.
(b) The formula for work is W = ΔK.E., where ΔK.E. represents the change in kinetic energy. To find the total work done on the ball as it moves from A to B, we need to calculate the change in kinetic energy:
ΔK.E. = K.E. at B - K.E. at A
= 6.0 J - 0.60 J
= 5.4 J
So, the total work done on the ball as it moves from A to B is 5.4 J.