A 3.5 kg block, initially in motion, is pushed along a horizontal floor by a force F of magnitude 17 N at an angle θ = 35° with the horizontal (Figure 6-20). The coefficient of kinetic friction between the block and floor is 0.25. (Assume the positive direction is to the right.)
Figure 6-20
(a) Calculate the magnitude of the frictional force on the block from the floor.
N
(b) Calculate the magnitude of the block's acceleration.
m/s2
for the magnitude all you do is 3.5*17cos35
To calculate the magnitude of the frictional force on the block from the floor, you need to use the equation:
frictional force = coefficient of kinetic friction * normal force
The normal force is the perpendicular force exerted by the floor on the block, which is equal to the weight of the block since the floor is horizontal. The weight is given by:
weight = mass * gravitational acceleration
In this case, the mass of the block is 3.5 kg and the gravitational acceleration is approximately 9.8 m/s^2.
So, weight = 3.5 kg * 9.8 m/s^2 = 34.3 N.
Now, you can calculate the normal force by taking the vertical component of the force F, which is given by:
normal force = weight * cos(θ)
Using the given angle θ = 35°, you can calculate the value of cos(35°) ≈ 0.819.
normal force = 34.3 N * 0.819 = 28.1 N.
Finally, plug in the coefficient of kinetic friction, which is 0.25, and the normal force, to calculate the frictional force:
frictional force = 0.25 * 28.1 N = 7.03 N.
Therefore, the magnitude of the frictional force on the block from the floor is 7.03 N.
To calculate the magnitude of the block's acceleration, you can use Newton's second law of motion, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration:
net force = mass * acceleration.
In this case, the net force is the horizontal component of the force F, which is given by:
net force = force * cos(θ).
Using the given force F = 17 N and angle θ = 35°, you can calculate the value of cos(35°) ≈ 0.819.
net force = 17 N * 0.819 = 13.9 N.
Now, since friction acts in the opposite direction of the force F, the net force can be written as:
net force = force - frictional force.
Substituting the values, you have:
13.9 N = 17 N - frictional force.
Solving for the frictional force:
frictional force = 17 N - 13.9 N = 3.1 N.
Finally, you can plug in the mass of the block, which is 3.5 kg, and the calculated frictional force, into the equation:
3.1 N = 3.5 kg * acceleration.
Rearranging the equation and solving for acceleration:
acceleration = 3.1 N / 3.5 kg ≈ 0.89 m/s^2.
Therefore, the magnitude of the block's acceleration is approximately 0.89 m/s^2.