A box of mass 14.3 kg with an initial velocity of 1.32 m/s slides down a plane, inclined at 20 with respect to the horizontal. The co efficient of kinetic friction is 0.51 The box stops after sliding a distance 017 (part 6 of 6) 10.0 points What is the magnitude of the average power generated by friction from start to stop?
A distance of what????
Initial Ke = (1/2) m v^2
Initial Pe relative to finish point = m g * (distance* sin 20)
Sum is Total initial energy
At the finish point both the Ke and the Pe are zero. Their sum is the work done by friction.
You otherwise could calculate that distance knowing the coef of friction
Friction force = mu m g cos 20
weight component down slope = m g sin 20
net force down slope = m g (sin 20 - mu cos 20) = m a
I assume a comes out negative (braking)
so at stop
0 = 1.32 + a t
solve for t
then average speed = 1.32 / 2
distance down slope = average speed * t
To find the magnitude of the average power generated by friction from start to stop, we need to calculate the work done by friction and divide it by the time it takes for the box to stop.
Let's break down the problem step by step:
Step 1: Calculate the gravitational force acting on the box.
The gravitational force is given by the formula: Fg = m * g, where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2). So, Fg = 14.3 kg * 9.8 m/s^2 = 140.14 N.
Step 2: Calculate the component of the gravitational force parallel to the inclined plane.
The component of the gravitational force parallel to the inclined plane is Fg_parallel = Fg * sin(θ), where θ is the angle of the inclined plane (20 degrees). So, Fg_parallel = 140.14 N * sin(20 degrees) = 47.7 N.
Step 3: Calculate the force of kinetic friction.
The force of kinetic friction is given by the formula: Ffriction = μ * Fg_parallel, where μ is the coefficient of kinetic friction (0.51). So, Ffriction = 0.51 * 47.7 N = 24.35 N.
Step 4: Calculate the work done by friction.
The work done by friction is given by the formula: W = Ffriction * d, where d is the distance the box slides before stopping (0.17 m). So, W = 24.35 N * 0.17 m = 4.1355 J.
Step 5: Calculate the time taken to stop.
The time taken to stop can be calculated using the equation of motion: v = u + at, where v is the final velocity (0 m/s), u is the initial velocity (1.32 m/s), a is the acceleration (which can be calculated using a = Fnet / m), and t is the time taken. The net force acting on the box is the difference between the gravitational force parallel to the plane and the force of friction, so Fnet = Fg_parallel - Ffriction.
First, calculate the net force: Fnet = 47.7 N - 24.35 N = 23.35 N.
Then, calculate the acceleration: a = Fnet / m = 23.35 N / 14.3 kg = 1.63 m/s^2.
Now, we can use the equation v = u + at to find t:
0 m/s = 1.32 m/s - 1.63 m/s^2 * t.
Solving for t, we get t = 0.81 s.
Step 6: Calculate the average power.
The average power can be calculated using the formula: P = W / t, where P is the average power, W is the work done, and t is the time taken. So, P = 4.1355 J / 0.81 s = 5.10 W.
Therefore, the magnitude of the average power generated by friction from start to stop is 5.10 Watts.