After placing a 0.500 m dent in the landlords van, the two management students are told they and
their 200 daN beer freezer have to go. The new ramp is inclined at an angle of 32.1
o
relative to
the horizontal. The coefficient of static friction between the freezer and the ramp is 0.800. Find the
minimum force required to move the box down the ramp if the force is applied:
(a) parallel to the ramp.
(b) horizontally.
To find the minimum force required to move the box down the ramp, we need to consider the forces acting on the box. In this case, we have two forces: the force of gravity acting downward and the force of friction acting parallel to the ramp.
(a) To find the minimum force required when the force is applied parallel to the ramp, we need to consider the component of the force of gravity that acts down the ramp. This force can be calculated using the formula:
Force_parallel = mass * acceleration_parallel
First, let's calculate the acceleration parallel to the ramp using trigonometry. We can find the magnitude of the acceleration by using the equation:
acceleration_parallel = gravity * sin(θ)
where θ is the angle of inclination of the ramp. In this case, θ is 32.1 degrees.
Then, we need to find the mass of the box. Given that the weight of the box is 200 daN (decanewton), we can convert it to kg since 1 daN is equal to 10 kg:
mass = weight / gravity
Substituting the values, we have:
mass = (200 daN) / (10 m/s^2)
Now, we can calculate the force parallel to the ramp:
Force_parallel = mass * acceleration_parallel
(b) To find the minimum force required when the force is applied horizontally, we need to consider the force of friction acting opposite to the applied force. The force of friction can be calculated using the formula:
Force_friction = coefficient_friction * normal_force
The normal force can be calculated using the equation:
normal_force = mass * gravity * cos(θ)
where θ is the angle of inclination of the ramp.
Once we have the force of friction, we can take it as the minimum force required to move the box horizontally.
Now, let's calculate the minimum force required using the given parameters:
(a) Force_parallel:
1. Calculate acceleration_parallel: acceleration_parallel = gravity * sin(32.1 degrees)
2. Calculate mass: mass = (200 daN) / (10 m/s^2)
3. Calculate Force_parallel: Force_parallel = mass * acceleration_parallel
(b) Force_friction for horizontal force:
1. Calculate normal_force: normal_force = mass * gravity * cos(32.1 degrees)
2. Calculate Force_friction: Force_friction = coefficient_friction * normal_force
Please provide the value of the coefficient of friction between the freezer and the ramp so that we can complete the calculations.