A 3.0 kg block, initially in motion, is pushed along a horizontal floor by a force F of magnitude 18 N at an angle = 45° with the horizontal. The coefficient of kinetic friction between the block and floor is 0.25. (Assume the positive direction is to the right.) Calculate the magnitude of the frictional force on the block from the floor. Calculate the magnitude of the block's acceleration.
* Physics/Math - bobpursley, Saturday, February 10, 2007 at 7:12pm
Break the force F in to vertical and horizontal components.
Friction= (mg + force vertical)mu
net force= ma
horizontal F - force friction = ma
* Physics/Math - COFFEE, Saturday, February 10, 2007 at 9:30pm
Ok, so this is what I tried...
T = uk*m*g / ((cos theta)+uk(sin theta))
T = ((.25)(3)(9.8)) / ((cos -45)+(.25)(sin -45))
T = 13.9 N
then,
FNet = m*g - T*sin(theta)
FNet = (3)(9.8) - (13.9)*(sin -45)
FNet = 39.2
then,
fk = uk*FNet
fk = .25*39.2
fk = 9.8
Well that was the wrong answer but I don't see anything wrong with my approach. Any suggestions??? PLEASE help .
I have no idea what you did.
Break the foroce F into horisontal components.
Forcevertical F*sintheta
Friction force= mu* (mg + F sinTheta)
Force horizonal= F * cosTheta
Force horizontal net=f*cosTheta-forcefriction
Now set that equal to mass*acceleration. Solve for acceleration
To solve this problem, we need to break down the forces and use Newton's second law (F = ma) to find the magnitude of the frictional force on the block and the block's acceleration.
First, we need to break the force F into horizontal and vertical components. The horizontal component is calculated as F * cos θ, and the vertical component is F * sin θ. In this case, F = 18 N and θ = 45°, so the horizontal component is 18 N * cos 45° and the vertical component is 18 N * sin 45°.
Next, we can calculate the magnitude of the frictional force using the equation: friction = μ * (mg + F * sin θ). Here, μ represents the coefficient of kinetic friction (given as 0.25), m represents the mass of the block (given as 3.0 kg), and g represents the acceleration due to gravity (approximately 9.8 m/s²).
Finally, using Newton's second law, we can set up the equation: net force = ma. The net force is the difference between the horizontal force and the frictional force. Rearranging the equation, we have: acceleration = (horizontal force - frictional force) / mass.
By following these steps and plugging in the given values, we can calculate the magnitude of the frictional force on the block from the floor and the magnitude of the block's acceleration.