A person has a choice while trying to move a crate across a horizontal pad of concrete: push it at a downward angle of 30 degrees, or pull it at an upward angle of 30 degrees.
If the crate has a mass of 50.0 kg and the coefficient of friction between it and the concrete is 0.750, calculate the force required to move it across the concrete at a constant speed in both situations.
m*g = 50 * 9.8 = 490 N. = Wt. of crate =
Normal force (Fn).
a. Fs = u*Fn + u*F*sin30
Fs = 0.75*490 + 0.375F = 367.5 + 0.375F
F*cosA-Fs = m*a
F*cos30-(367.5+0.375F) = m*0 = 0
0.866F-367.5-0.375F = 0
0.866F-0.375F = 367.5
0.491F = 367.5
F = 748.5 N
b. Fs = 0.75*490 - 0.75*F*sin30
Fs = 367.5 - 0.375F
F*cos30-(367.5-0.375F) = m*0 = 0
0.866F-367.5+0.375F = 0
1.241F = 367.5
F = 296.1 N.
thanks Henry!
To calculate the force required to move the crate across the concrete at a constant speed, we can use the concept of forces and Newton's second law of motion.
In both situations (pushing and pulling), the force required to overcome the frictional force can be determined using the equation:
Force = Frictional force
The frictional force (Ff) can be calculated using the equation:
Ff = coefficient of friction * Normal force
The normal force (Fn) is the force exerted by the surface perpendicular to the surface of contact. In this case, it is equal to the weight of the crate, which is given by the equation:
Weight = mass * acceleration due to gravity
Where acceleration due to gravity (g) is approximately 9.8 m/s^2.
Let's calculate the force required to move the crate in each situation.
1. Pushing at a downward angle of 30 degrees:
First, we need to resolve the downward force applied into vertical and horizontal components. The vertical component will be equal to the weight of the crate:
Weight = mass * acceleration due to gravity
= 50.0 kg * 9.8 m/s^2
= 490 N
The horizontal component will be equal to:
Horizontal force = Force applied * cos (angle)
Since the angle is given as 30 degrees, we calculate the horizontal force:
Horizontal force = Force applied * cos(30 degrees) = Force applied * 0.866
Next, we calculate the frictional force:
Ff = coefficient of friction * Normal force
= 0.750 * (Weight - Vertical force)
= 0.750 * (490 N - Horizontal force)
Since we want to move the crate at a constant speed, the force applied must be equal to the frictional force:
Force applied = Ff
= 0.750 * (490 N - Horizontal force)
2. Pulling at an upward angle of 30 degrees:
Similar to the previous situation, we resolve the upward force applied into vertical and horizontal components. The vertical component will be equal to:
Vertical force = Force applied * sin (angle)
Since the angle is given as 30 degrees, we calculate the vertical force:
Vertical force = Force applied * sin(30 degrees) = Force applied * 0.5
The horizontal component will be equal to the force applied. Therefore, the horizontal force will be equal to:
Horizontal force = Force applied
Next, we calculate the frictional force:
Ff = coefficient of friction * Normal force
= 0.750 * (Weight + Vertical force)
= 0.750 * (490 N + Vertical force)
Again, to move the crate at a constant speed, the force applied must be equal to the frictional force:
Force applied = Ff
= 0.750 * (490 N + Vertical force)
These are the calculations to determine the force required to move the crate across the concrete at a constant speed in both situations.
To calculate the force required to move the crate across the concrete at a constant speed, we need to consider the forces acting on the crate. These forces include the force of gravity (weight of the crate), the normal force exerted by the concrete, and the force of friction.
Let's start by calculating the force of gravity, which is given by the equation F_gravity = m * g, where m is the mass of the crate and g is the acceleration due to gravity (approximately 9.8 m/s^2).
F_gravity = 50.0 kg * 9.8 m/s^2
F_gravity = 490 N
Next, we need to calculate the normal force. The normal force is equal to the force of gravity when the crate is on a horizontal surface, so the normal force is also 490 N.
Now we can calculate the force of friction using the equation F_friction = μ * F_normal, where μ is the coefficient of friction.
F_friction = 0.750 * 490 N
F_friction = 367.5 N
The force required to move the crate at a constant speed is equal to the force of friction. Therefore, the force required to move the crate in both situations (pushing and pulling) is 367.5 N.
Please note that given the same coefficient of friction and mass of the crate, the force required to move the crate at a constant speed is the same regardless of the pushing or pulling angle. In this case, both pushing and pulling require the same amount of force.