A 10.2 kg crate is pulled up a rough incline
with an initial speed of 1.5 m/s. The pulling
force is 123.0 N parallel to the incline, which
makes an angle of 14.6◦ with the horizontal.
The coe�cient of kinetic friction is 0.39 and
the crate is pulled a distance of 8.1 m.
The acceleration of gravity is 9.81 m/s2 .
a) Find the work done by Earth’s gravity
on the crate. Answer in units of J.
017 (part 2 of 5) 10.0 points
b) Find the work done by the force of friction
on the crate. Answer in units of J.
work done by gravity is mgh where h is the increase in altitude.
here h = 8.1 sin 14.6
h = 2.04 meters
so
U = 10.2 kg * 9.8 m/s^2 * 2.04m = 100 N *2.04 meters = 204 J
work done by friction = friction forcve in Newtons * 8.1 meters
friction force = .39 * 100 N *cos 14.6 = 37.7 Newtons
37.7 * 8.1 = 306 Joules
To solve these problems, we need to use the concepts of work and energy. The work done by a force is given by the equation:
Work = Force * Distance * cos(theta)
where Force is the magnitude of the force, Distance is the distance over which the force acts, and theta is the angle between the force and the direction of motion.
a) To find the work done by Earth's gravity on the crate, we first need to calculate the force of gravity acting on the crate. The force of gravity is given by the equation:
Force of gravity = mass * acceleration due to gravity
where mass is the mass of the crate and acceleration due to gravity is the acceleration experienced by objects near the surface of the Earth. In this case, mass = 10.2 kg and acceleration due to gravity = 9.81 m/s^2, so the force of gravity on the crate is:
Force of gravity = 10.2 kg * 9.81 m/s^2
Next, we calculate the distance over which the force of gravity acts. This distance is equal to the vertical height through which the crate is pulled. In this case, we are not given the vertical height, but we are given the distance along the incline (8.1 m) and the angle of the incline (14.6 degrees). We can calculate the vertical height using the equation:
Vertical height = Distance * sin(theta)
Vertical height = 8.1 m * sin(14.6 degrees)
Now, we can calculate the work done by Earth's gravity:
Work = Force of gravity * Vertical height * cos(0 degrees)
b) To find the work done by the force of friction on the crate, we need to calculate the force of friction. The force of friction is given by the equation:
Force of friction = coefficient of kinetic friction * magnitude of the normal force
The magnitude of the normal force can be calculated using the equation:
Normal force = mass * acceleration due to gravity * cos(theta)
Substitute the given values into the equations and calculate the work done by the force of friction:
Work = Force of friction * Distance * cos(theta)