A block of mass m = 5.4 kg is pulled up a = 23 incline as in the figure with a force of magnitude F = 35 N. Find the acceleration of the block if the incline is frictionless.
force down the plane due to weight= mg*cosTheta
net force= 35-mg*cosTheta=ma
solve for acceleration a.
thanks, this really helped.. but i had to use sin instead of cos
To find the acceleration of the block, we will use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force acting on the block is the force applied that pulls it up the incline.
The force pulling the block up the incline is given as F = 35 N. Since the incline is frictionless, there is no opposing force due to friction.
The force component acting parallel to the incline can be calculated as:
F_parallel = F * sin(θ)
Where θ is the angle of the incline.
Given that the incline angle is α = 23 degrees, the force component acting parallel to the incline is:
F_parallel = 35 N * sin(23°)
Now, we can calculate the acceleration of the block using Newton's second law:
F_parallel = m * a
Where:
m is the mass of the block (m = 5.4 kg)
a is the acceleration of the block
Rearranging the equation, we have:
a = F_parallel / m
Let's substitute the values and calculate the acceleration:
F_parallel = 35 N * sin(23°)
m = 5.4 kg
a = (35 N * sin(23°)) / 5.4 kg
Using a calculator, we can find the value of a to be approximately 1.66 m/s^2.
Therefore, the acceleration of the block when the incline is frictionless is 1.66 m/s^2.
To find the acceleration of the block, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's define the forces acting on the block:
1. The gravitational force acting vertically downward is given by the formula: F_gravity = m * g, where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. The force pulling the block up the incline is F_applied = 35 N.
3. There is no friction acting on the block since the incline is described as being frictionless.
Now, let's break down the gravitational force into two components: one parallel to the incline and one perpendicular to the incline.
The component of the gravitational force parallel to the incline is F_parallel = m * g * sin(θ), where θ is the angle of the incline (23 degrees in this case).
The net force acting on the block along the incline is the difference between the force pulling the block up the incline (F_applied) and the component of the gravitational force parallel to the incline (F_parallel):
F_net = F_applied - F_parallel
Since the net force is equal to the mass of the block multiplied by its acceleration, we have:
F_net = m * a
Applying this to the given values and equation, we can solve for the acceleration (a):
m * a = F_net
m * a = F_applied - F_parallel
a = (F_applied - F_parallel) / m
Now, substitute the values provided into the equation and calculate the acceleration (a).