An object with a mass of 32 kg has an initial energy of 500 J. At the end of the experiment, the velocity of the object is recorded as 5.1 m/s. If the object travelled 50 m to get to this point, what was the average force of friction on object during the trip? Assume no potential energy.
I've bee stuck on this question, can whoever helps me show the work behind it? I have a lot of practice questions like this and I want to be able to do them myself.
I don't understand @R_scott
To find the average force of friction on the object during the trip, we need to use the Work-Energy theorem. The Work-Energy theorem states that the work done on an object by a net force is equal to the change in the object's kinetic energy.
First, let's calculate the final kinetic energy of the object using the given mass and velocity:
Kinetic energy (K) = 0.5 * mass * velocity^2
K = 0.5 * 32 kg * (5.1 m/s)^2
K = 0.5 * 32 kg * 26.01 m^2/s^2
K = 416.32 J
Now, let's calculate the work done by the net force during the trip using the initial and final energies:
Work done (W) = Change in kinetic energy (ΔK)
W = K_final - K_initial
W = 416.32 J - 500 J
W = -83.68 J
The negative sign indicates that work is done against the force of friction, which opposes the motion of the object.
Next, let's calculate the displacement during the trip, given as 50 m.
To find the average force of friction, we can use the formula:
W = force * displacement * cos(theta)
In this case, since the friction force and displacement are in the same direction (opposite to motion), the angle (theta) between them is 0 degrees. Therefore, cos(theta) = 1.
Substituting the given values into the formula, we have:
-83.68 J = force * 50 m * 1
force = -83.68 J / 50 m
force = -1.674 N
The negative sign indicates that the force of friction acts opposite to the direction of motion. Suppose you prefer positive quantities, you can ignore the sign, and the average force of friction on the object during the trip would be approximately 1.674 N.
Sure! To find the average force of friction on the object during the trip, we can use the work-energy principle. The work done on an object is equal to the change in its kinetic energy.
In this scenario, the initial energy of the object is 500 J, and its final kinetic energy is given by the formula: KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.
Given:
Mass of the object, m = 32 kg
Initial energy, E_initial = 500 J
Final velocity, v = 5.1 m/s
Distance traveled, d = 50 m
First, we need to find the final kinetic energy of the object:
KE_final = (1/2)mv^2
= (1/2)(32 kg)(5.1 m/s)^2
Next, we calculate the work done on the object:
Work = KE_final - E_initial
Substituting the values:
Work = [(1/2)(32 kg)(5.1 m/s)^2] - 500 J
Now, let's calculate the force using the work-energy principle:
Work = Force × distance
Rearranging the equation:
Force = Work / distance
Substituting the known values:
Force = [(1/2)(32 kg)(5.1 m/s)^2] - 500 J / 50 m
Evaluating the expression:
Force ≈ 164.544 N
Therefore, the average force of friction on the object during the trip is approximately 164.544 N.
final K.E = 1/2 * 32 * 5.1^2
work = (initial K.E.) - (final K.E.)
also ... work = force * distance = f * 50 m
... substitute the work value and solve for f