Jason works for a moving company. A 95 kg wooden crate is sitting on the wooden ramp of his truck, the ramp is angled at 11 degrees.
What is the magnitude of force, directed parallel to the ramp, that he needs to get it to start moving up the ramp?
What is the magnitude of force, directed parallel to the ramp, that he needs to get it to start moving down the ramp?
Well, Jason might need a little help from the circus for this one! To calculate the magnitude of force needed to get the wooden crate moving up the ramp, we can use the following formula:
Force_up = mass * acceleration
Given that the crate weighs 95 kg and the ramp is angled at 11 degrees, we need to break that down into components. The force due to gravity acting on the crate can be divided into two directions: one parallel to the ramp (force_up) and the other perpendicular to the ramp.
For a ramp angle of 11 degrees, the perpendicular force can be calculated as follows:
Force_perpendicular = mass * gravity * sin(angle)
Now we can calculate the parallel force needed to move the crate up the ramp by multiplying the perpendicular force by the coefficient of static friction (since we want it to start moving):
Force_up = Force_perpendicular * coefficient_of_static_friction
To find the coefficient of static friction, we would need more information about the surfaces in contact. But for now, let's hope Jason doesn't find himself sliding down the ramp on a wooden crate!
Now, let's talk about the magnitude of force needed to get the crate moving down the ramp. In this case, we need to take into account the force due to gravity acting in the opposite direction and subtract it from the frictional force acting up the ramp.
So, in a nutshell, to answer your question about the magnitude of force, I'm going to need a little more information. Or maybe I'll just call in the clowns to help us out! 🤡
To find the magnitude of force needed to get the crate to start moving up the ramp, we need to calculate the force required to overcome the gravitational force pulling it downwards. The force required can be found using the following formula:
Force_up = Mass * Acceleration
The acceleration can be calculated as the component of gravity acting parallel to the ramp, which is given by:
Acceleration = Gravity * sin(angle)
where the angle is given as 11 degrees.
Now, let's calculate the required force:
Mass = 95 kg
Gravity = 9.8 m/s^2
Acceleration_up = Gravity * sin(angle)
= 9.8 * sin(11 degrees)
Finally, we can calculate the force needed:
Force_up = Mass * Acceleration_up
Okay, now let's calculate the magnitude of the force needed to get the crate to start moving down the ramp.
The force required to start moving down the ramp would be equal to the force component required to overcome the gravitational force acting parallel to the ramp:
Force_down = Mass * Acceleration_down
Acceleration_down = Gravity * sin(angle)
= 9.8 * sin(11 degrees)
So, we can now calculate the required force:
Force_down = Mass * Acceleration_down
To determine the magnitude of force that Jason needs to get the wooden crate to start moving up or down the ramp, we need to consider the forces acting on the crate.
First, let's analyze the forces when the crate is on an inclined plane (the ramp). We have two main forces at play: the force of gravity pulling the crate downward (its weight), and the normal force exerted by the ramp on the crate perpendicular to the ramp's surface.
1. Force to start moving up the ramp:
When Jason wants to start moving the crate up the ramp, he needs to overcome the force of gravity pulling it downward. The component of the force of gravity along the ramp's surface contributes to this force. This force is given by the equation:
Force up the ramp = force of gravity parallel to the ramp = m * g * sin(theta),
where:
- m is the mass of the crate (95 kg),
- g is the acceleration due to gravity (approximately 9.8 m/s^2),
- theta is the angle of the ramp (11 degrees).
Substituting these values into the equation, we have:
Force up the ramp = 95 kg * 9.8 m/s^2 * sin(11 degrees).
Force up the ramp = 163.46 N.
Therefore, Jason needs a force of approximately 163.46 newtons directed parallel to the ramp to get the crate to start moving up the ramp.
2. Force to start moving down the ramp:
When Jason wants to start moving the crate down the ramp, he needs to overcome the force of gravity pulling it downward and assist the crate in its motion. In this case, the component of the force of gravity that opposes the motion (in the direction down the ramp) contributes to this force. This force is given by:
Force down the ramp = force of gravity parallel to the ramp = m * g * sin(theta),
using the same values as above.
Substituting these values into the equation, we have:
Force down the ramp = 95 kg * 9.8 m/s^2 * sin(11 degrees).
Force down the ramp = 163.46 N.
Therefore, Jason needs a force of approximately 163.46 newtons directed parallel to the ramp to get the crate to start moving down the ramp.
a. M*g = 95 * 9.8 = 931 N. = Wt. of crate.
Fp = 931**sin11=178 N. = Force parallel to incline.
Fn = 931*Cos11 = 914 N. = Normal force.
u = 0.40? = coefficient of starting friction.
Fs = u*Fn = 0.4 * 914 = 366 N. = Force of starting friction.
F-Fp-Fs = M*a.
F-178-366 = 95*0,
F = 544 N.
b. F+Fp-Fs = M*a.
F+178-366 = 95*0.
F =