you slide a 325N trunk up a 20 degree inclined plane w/ constant velocity by exerting a force of 211 N parallel to the inclined plane
a) what is the comp. of the trunk's weight parallel to the plane?
b) what is the sum of the Fa, friction and the parallel comp. of the trunk's weight? Why?
c) What is the size and direct. of the Ff?
d) What is the coeff. of friction?
a) 325 sin 20
b) it is not accelerating so the sum of forces in any direction is zero.
c)Call x positive up the plane.
The thing is moving up the plane, in the plus x direction
the friction force resists the motion so it acts down the plane, in the -x direction
Sum all forces to get the friction force
Force down ramp due to friction = Ff
Force down ramp due to gravity = 325 sin 20 N
Force up ramp due to you = 211 N
Sum of forces up ramp = 0
211 -Ff - 325 sin 20 = 0
solve for Ff directed down ramp
Ff = coef *325 cos 20
we just got Ff so solve for coef
a) The component of the trunk's weight parallel to the plane can be determined using trigonometry. We can use the formula:
Weight_parallel = Weight * sin(angle)
Weight_parallel = 325 N * sin(20°)
b) The sum of Fa (force exerted), friction, and the parallel component of the trunk's weight should be zero, as the trunk is moving with constant velocity. This means that the force you exert (211 N) balances out the frictional force and the parallel component of the trunk's weight.
c) To find the size and direction of the frictional force (Ff), we need to consider that it is equal and opposite to the force exerted parallel to the inclined plane. Therefore, Ff = 211 N and its direction is opposite to the applied force.
d) To find the coefficient of friction (μ), we need to divide the magnitude of the frictional force (Ff) by the magnitude of the normal force (N) exerted by the inclined plane on the trunk. Since the trunk is on the inclined plane, the normal force is equal to the weight of the trunk, which is 325 N.
μ = Ff / N
μ = 211 N / 325 N
To answer these questions, we first need to understand some basic principles of physics, such as forces, inclined planes, and friction. We'll go through each question step by step.
a) What is the component of the trunk's weight parallel to the plane?
The component of the trunk's weight parallel to the inclined plane can be found using trigonometry. We can use the equation: Frictional Force = Weight * sin(angle), where the angle is 20 degrees. The weight is given as 325 N, so we can substitute the values into the equation to find the answer.
Frictional Force = 325 N * sin(20 degrees)
Frictional Force = 110.86 N (rounded to two decimal places)
Therefore, the component of the trunk's weight parallel to the plane is approximately 110.86 N.
b) What is the sum of Fa, friction, and the parallel component of the trunk's weight? Why?
To find the sum of these forces, we add up all the forces acting in the same direction. In this case, the forces acting in the same direction are the parallel component of the trunk's weight and the force exerted parallel to the inclined plane.
Sum of forces = Force exerted + parallel component of weight
Sum of forces = 211 N + 110.86 N
Sum of forces = 321.86 N (rounded to two decimal places)
The reason we add these forces is that when the trunk is moving at constant velocity (i.e., not accelerating), the sum of the forces acting in the direction of motion must be zero. This is known as the equilibrium condition.
c) What is the size and direction of the frictional force?
The size of the frictional force can be found by multiplying the coefficient of friction (μ) by the normal force. However, we need to calculate the normal force first. The normal force is equal in magnitude but opposite in direction to the perpendicular component of the trunk's weight. We can find it using the equation: Normal force = Weight * cos(angle), where the angle is 20 degrees.
Normal force = 325 N * cos(20 degrees)
Normal force = 305.02 N (rounded to two decimal places)
Now we can find the size of the frictional force:
Frictional force = Coefficient of friction * Normal force
From the given information, we can't directly find the coefficient of friction. We'll come back to this in the last question.
d) What is the coefficient of friction?
To determine the coefficient of friction, we need additional information. The coefficient of friction is the ratio of the force of friction to the normal force. Normally, experimental data is required to determine the coefficient of friction. If we had the value of the force of friction, we could use it to calculate the coefficient of friction by dividing it by the normal force.
However, in this case, we don't have the force of friction itself. So, without the required information, we can't determine the coefficient of friction.
A) 325sin(20)=111N
B) 0 -- because it's going in a constant velocity.
C)?
D)?