Physics Hwk. Problem: Frictional Force

[shawonna23]

I am really stuck on how to even start solving this problem, can someone help me please!

A 2.5 kg block is pushed along a horizontal floor by a force F of magnitude 17 N at an angle = 35° with the horizontal. The coefficient of kinetic friction between the block and floor is 0.25.

a.Calculate the magnitude of the frictional force on the block from the floor.
b.Calculate the magnitude of the acceleration of the block.

 

[Andrew Mason]

A 2.5 kg block is pushed along a horizontal floor by a force F of magnitude 17 N at an angle = 35° with the horizontal. The coefficient of kinetic friction between the block and floor is 0.25.

a.Calculate the magnitude of the frictional force on the block from the floor.
b.Calculate the magnitude of the acceleration of the block.

The force F provides a downward component and a horizontal component. Work out the magnitude of each component.

The downward component provides additional normal force (in addition to mg). The normal force determines the horizontal frictional force:

The acceleration is determined by the horizontal component of F minus the horizontal friction force.

AM

 

[thepatientmental]

To start solving this problem, you need to first draw a free body diagram of the block. This will help you visualize all the forces acting on the block. The force F is the pushing force applied at an angle of 35°, and the frictional force is acting in the opposite direction of the motion. The weight of the block, which is equal to its mass (2.5 kg) multiplied by the gravitational acceleration (9.8 m/s^2), is acting downwards.

Now, to calculate the magnitude of the frictional force, you can use the formula Ff = μN, where μ is the coefficient of kinetic friction and N is the normal force. The normal force is equal to the weight of the block, so we can substitute that in the formula. Thus, Ff = (0.25)(2.5 kg)(9.8 m/s^2) = 6.125 N. This is the magnitude of the frictional force on the block from the floor.

To calculate the acceleration of the block, we can use Newton's Second Law, which states that the net force on an object is equal to its mass multiplied by its acceleration (F = ma). In this case, the net force is the pushing force F minus the frictional force Ff, so we can write the equation as F - Ff = ma. We know the values for F and Ff, so we can substitute them in the equation. Thus, 17 N - 6.125 N = (2.5 kg)a. Solving for a, we get a = 4.35 m/s^2. This is the magnitude of the acceleration of the block.

I hope this helps you get started on solving the problem. Remember to always draw a free body diagram and use relevant equations to solve physics problems. Good luck!