A 3.8 kg ball is rolling along a slippery road at 1.5 m/s E. It then rolls onto a patch of grass and slows to a stop over a distance of 3.6 m
a) calculate the total work on the ball
b) calculate the net force that caused the ball to come to a stop (force is constant)
4.275J
a) To calculate the total work done on the ball, you can use the work-energy principle which states that the work done on an object is equal to the change in its kinetic energy.
The initial kinetic energy (KEi) of the ball can be calculated using the equation:
KEi = (1/2) * mass * velocity^2
Plugging in the values, we have:
KEi = (1/2) * 3.8 kg * (1.5 m/s)^2
Next, we need to find the final kinetic energy (KEf) of the ball. Since the ball comes to a stop, its final kinetic energy is zero.
The change in kinetic energy (ΔKE) is then:
ΔKE = KEf - KEi
= 0 - [(1/2) * 3.8 kg * (1.5 m/s)^2]
Finally, the total work (W) done on the ball is equal to the change in kinetic energy:
W = ΔKE
= -[(1/2) * 3.8 kg * (1.5 m/s)^2] <--- Note that the negative sign indicates that work is done on the ball.
b) Since the ball comes to a stop, the net force acting on it is responsible for decelerating it to zero velocity. To calculate the net force, you can use Newton's second law, which states that the net force is equal to the mass of an object multiplied by its acceleration.
In this case, we can use the following equation to calculate the net force (F):
F = mass * acceleration
Since the ball comes to a stop, its final velocity is zero. We can use the following equation to relate the initial velocity (vi), final velocity (vf), and acceleration (a):
vf^2 = vi^2 + 2aΔx
Since vf = 0 m/s, we can rearrange the equation to solve for acceleration (a):
0 = vi^2 + 2aΔx
a = -vi^2 / (2Δx)
Now we can calculate the net force using the equation:
F = mass * acceleration
= 3.8 kg * [-vi^2 / (2Δx)]
Substituting the given values, we get:
F = 3.8 kg * [- (1.5 m/s)^2 / (2 * 3.6 m)]