After pushing a 22.2 kg kid and tricycle over 10.3 m of smooth, level sidewalk from rest, the "combo" is moving at 3.0 m/s. Find the combo's kinetic energy. (the answer is 99.9j) what net force must have been delivered to the combo?Now you stop pushing and let the combo coast to a stop. The only force stopping the combo is the force of friction. If the force of friction is 7.9 N, how far will the combo coast before it stops?
To find the combo's kinetic energy, you can use the formula:
Kinetic energy (KE) = 1/2 * mass * velocity^2
Plugging in the given values:
Mass (m) = 22.2 kg
Velocity (v) = 3.0 m/s
KE = 1/2 * 22.2 kg * (3.0 m/s)^2
KE = 1/2 * 22.2 kg * 9 m^2/s^2
KE ≈ 99.9 J
So the combo's kinetic energy is approximately 99.9 Joules.
To find the net force delivered to the combo, you can use Newton's second law:
Net force (F) = mass (m) * acceleration (a)
We are given the mass (m) as 22.2 kg, and we can calculate the acceleration (a) using the equation:
a = (final velocity - initial velocity) / time
Since the combo starts from rest, the initial velocity is 0 m/s and the final velocity is 3.0 m/s. Let's assume it takes a time of t seconds to reach this final velocity.
a = (3.0 m/s - 0 m/s) / t
a = 3.0 m/s / t
Plugging the acceleration into Newton's second law:
F = 22.2 kg * (3.0 m/s / t)
F = 66.6 kg*m/s / t
Unfortunately, we don't have enough information to determine the exact value of the net force. We need the value of time (t) to calculate it.
To find the combo's kinetic energy, we can use the formula:
Kinetic Energy (KE) = (1/2) * mass * velocity^2
Given:
Mass (m) = 22.2 kg
Velocity (v) = 3.0 m/s
Substituting the given values into the formula, we get:
KE = (1/2) * 22.2 kg * (3.0 m/s)^2
= 0.5 * 22.2 kg * 9.0 m^2/s^2
= 99.9 J
Therefore, the combo's kinetic energy is 99.9 Joules.
To determine the net force required to accelerate the combo, we can use Newton's second law of motion:
Net Force (F_net) = mass * acceleration
Since the combo was initially at rest and then accelerated to a velocity of 3.0 m/s, we can calculate the acceleration using the formula:
Acceleration (a) = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 0 m/s
Final velocity (v) = 3.0 m/s
Time (t) = Not provided
The time it takes for the combo to reach a velocity of 3.0 m/s is not given, so we cannot calculate the exact acceleration. However, if we assume it took 2 seconds to reach that velocity, we can proceed with the calculation. Keep in mind that this assumption may not be accurate.
Using the assumed time of 2 seconds:
Acceleration (a) = (3.0 m/s - 0 m/s) / 2 s
= 3.0 m/s / 2 s
= 1.5 m/s^2
Now we can calculate the net force:
F_net = mass * acceleration
= 22.2 kg * 1.5 m/s^2
= 33.3 N
Therefore, the net force delivered to the combo is 33.3 Newtons.
Finally, to determine the distance the combo will coast before stopping, we need to use the force of friction. The force of friction can be calculated using the formula:
Force of Friction (F_friction) = coefficient of friction * normal force
The normal force is equal to the weight of the combo, which is given by:
Weight (W) = mass * gravitational acceleration
Given:
Mass (m) = 22.2 kg
Gravitational acceleration (g) = 9.8 m/s^2
Weight (W) = 22.2 kg * 9.8 m/s^2
= 217.56 N
Now we can calculate the force of friction using the given value:
Force of Friction (F_friction) = 7.9 N
Since the only force stopping the combo is the force of friction, we can equate the force of friction to the net force:
F_friction = F_net
Rearranging the equation, we get:
F_net = F_friction = 7.9 N
Now, we can use the concept of work-energy theorem:
Work (W) = Force * Distance
The work done by the force of friction will reduce the kinetic energy of the combo to zero, therefore:
Work (W) = Change in kinetic energy (KE)
Since the work done is equal to the force of friction multiplied by the distance traveled, we can calculate the distance:
Distance = Work / Force of Friction
Distance = (Change in kinetic energy) / Force of Friction
Change in kinetic energy (ΔKE) = Initial KE - Final KE
= KE - 0 (since the final kinetic energy is zero when the combo is at rest)
Using the previously calculated value of kinetic energy (KE = 99.9 J), we get:
ΔKE = 99.9 J - 0
= 99.9 J
Distance = 99.9 J / 7.9 N
= 12.65 m (approximately, rounded to two decimal places)
Therefore, the combo will coast approximately 12.65 meters before it comes to a stop.